https://conference.portonvictor.org/w/api.php?action=feedcontributions&user=Victor+Porton&feedformat=atomVirtual scientific conference - User contributions [en]2021-03-07T08:32:12ZUser contributionsMediaWiki 1.31.2https://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=420Can Human Rights Be Accomplished Experiment/Events2019-08-22T09:46:57Z<p>Victor Porton: </p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''14 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment<br />
<br />
'''24 June 2019'''<br />
<br />
Received a (delayed more than allowed by the law) reply from Kirovskiy district court of Perm city. I do not upload the reply because it contains nothing interesting except of a denial of the request and the advice to apply to a Moscow court where the Ministry of Finances is located.<br />
<br />
As I have already applied (after the delay expired illegally) to exactly the same court, I am doing nothing additional.<br />
<br />
It seems now impossible to check if the first court replied during my letters to presidents, Human Rights Watch, etc. or it was just a regular delay. The experiment purpose now seems optimistic to attain.<br />
<br />
'''28 Jun 2019'''<br />
<br />
Received a reply from Internal Affairs Ministry of Russia saying that it is not in their competence.<br />
<br />
'''21 July 2019'''<br />
<br />
Send to Putin:<br />
<br />
:Dear Putin,<br />
:<br />
:I filed a lawsuit (attached) on June 21 in the Tverskoy District Court of Moscow.<br />
:<br />
:The claim is ignored.<br />
:<br />
:I will demand sanctions against Russia if you do not ensure non-ignoring the law, since Russia is an illusion: unable to respond to emails. No pity.<br />
<br />
'''22 Aug 2019'''<br />
<br />
Жалоба в московскую квалификационную коллегию судей:<br />
<br />
Мною был подан 21 июня 1029 гражданский иск в Тверской районный суд г. Москвы (прилагается).<br />
<br />
Иск был передан судье Солопове Ольге Николаевне. В установленные законом сроки (с большим запасом) ответ на иск не был прислан. Таким образом вопиющим образом нарушен закон.<br />
<br />
Мышление Солоповой Ольги понятно и очевидно:<br />
<br />
Дело смешное и постыдное. Юмор и стыд имеют приоритет над законом. Поэтому выполнять закон не следует.<br />
<br />
Требую передать мое дело другому судье.<br />
<br />
Требую возбудить уголовное дело против Солоповой Ольги о халатности.<br />
<br />
Требую признать Солопову Ольгу невменяемой, в силу того, что стыд сделал нормальное функционирование ее мозга невозможным, в частности она оказалась не в состоянии отвечать на сообщения.<br />
<br />
Таким образом, Солопова Ольга не способна отвечать: ни по закону, ни на сообщения.<br />
<br />
--<br />
<br />
I also have sent [https://portonrus.files.wordpress.com/2019/08/iskovoje-zajavlenie-1-straniza.doc this appeal] to the Moscow Arbitration Court. The answer followed very quickly and was that the appeal should be sent to the court where Solopova is the chairman. The Russian parliament members need psychiatric help, too: They set to appeal against a chairman of a court to him/her- self! Currently, I am not going to send this appeal as useless.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=419Can Human Rights Be Accomplished Experiment/Events2019-08-22T04:36:23Z<p>Victor Porton: </p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''14 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment<br />
<br />
'''24 June 2019'''<br />
<br />
Received a (delayed more than allowed by the law) reply from Kirovskiy district court of Perm city. I do not upload the reply because it contains nothing interesting except of a denial of the request and the advice to apply to a Moscow court where the Ministry of Finances is located.<br />
<br />
As I have already applied (after the delay expired illegally) to exactly the same court, I am doing nothing additional.<br />
<br />
It seems now impossible to check if the first court replied during my letters to presidents, Human Rights Watch, etc. or it was just a regular delay. The experiment purpose now seems optimistic to attain.<br />
<br />
'''28 Jun 2019'''<br />
<br />
Received a reply from Internal Affairs Ministry of Russia saying that it is not in their competence.<br />
<br />
'''21 July 2019'''<br />
<br />
Send to Putin:<br />
<br />
:Dear Putin,<br />
:<br />
:I filed a lawsuit (attached) on June 21 in the Tverskoy District Court of Moscow.<br />
:<br />
:The claim is ignored.<br />
:<br />
:I will demand sanctions against Russia if you do not ensure non-ignoring the law, since Russia is an illusion: unable to respond to emails. No pity.<br />
<br />
'''22 Aug 2019'''<br />
<br />
Жалоба в московскую квалификационную коллегию судей:<br />
<br />
Мною был подан 21 июня 1029 гражданский иск в Тверской районный суд г. Москвы (прилагается).<br />
<br />
Иск был передан судье Солопове Ольге Николаевне. В установленные законом сроки (с большим запасом) ответ на иск не был прислан. Таким образом вопиющим образом нарушен закон.<br />
<br />
Мышление Солоповой Ольги понятно и очевидно:<br />
<br />
Дело смешное и постыдное. Юмор и стыд имеют приоритет над законом. Поэтому выполнять закон не следует.<br />
<br />
Требую передать мое дело другому судье.<br />
<br />
Требую возбудить уголовное дело против Солоповой Ольги о халатности.<br />
<br />
Требую признать Солопову Ольгу невменяемой, в силу того, что стыд сделал нормальное функционирование ее мозга невозможным, в частности она оказалась не в состоянии отвечать на сообщения.<br />
<br />
Таким образом, Солопова Ольга не способна отвечать: ни по закону, ни на сообщения.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=MediaWiki:Sitenotice&diff=392MediaWiki:Sitenotice2019-08-03T11:39:16Z<p>Victor Porton: </p>
<hr />
<div>Publish here. '''[https://crypto4ngo.org/project/view/5 Donate]''' <div style="float:right"><addthis /></div></div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=MediaWiki:Sitenotice&diff=391MediaWiki:Sitenotice2019-08-03T04:36:30Z<p>Victor Porton: Created page with "Publish here. '''Donate''' <div style="float:right"><addthis /></div>"</p>
<hr />
<div>Publish here. '''[[Project:Donate|Donate]]''' <div style="float:right"><addthis /></div></div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=367Can Human Rights Be Accomplished Experiment/Events2019-07-21T05:41:37Z<p>Victor Porton: </p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''14 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment<br />
<br />
'''24 June 2019'''<br />
<br />
Received a (delayed more than allowed by the law) reply from Kirovskiy district court of Perm city. I do not upload the reply because it contains nothing interesting except of a denial of the request and the advice to apply to a Moscow court where the Ministry of Finances is located.<br />
<br />
As I have already applied (after the delay expired illegally) to exactly the same court, I am doing nothing additional.<br />
<br />
It seems now impossible to check if the first court replied during my letters to presidents, Human Rights Watch, etc. or it was just a regular delay. The experiment purpose now seems optimistic to attain.<br />
<br />
'''28 Jun 2019'''<br />
<br />
Received a reply from Internal Affairs Ministry of Russia saying that it is not in their competence.<br />
<br />
'''21 July 2019'''<br />
<br />
Send to Putin:<br />
<br />
:Dear Putin,<br />
:<br />
:I filed a lawsuit (attached) on June 21 in the Tverskoy District Court of Moscow.<br />
:<br />
:The claim is ignored.<br />
:<br />
:I will demand sanctions against Russia if you do not ensure non-ignoring the law, since Russia is an illusion: unable to respond to emails. No pity.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=352Can Human Rights Be Accomplished Experiment/Events2019-06-28T09:17:05Z<p>Victor Porton: </p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''14 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment<br />
<br />
'''24 June 2019'''<br />
<br />
Received a (delayed more than allowed by the law) reply from Kirovskiy district court of Perm city. I do not upload the reply because it contains nothing interesting except of a denial of the request and the advice to apply to a Moscow court where the Ministry of Finances is located.<br />
<br />
As I have already applied (after the delay expired illegally) to exactly the same court, I am doing nothing additional.<br />
<br />
It seems now impossible to check if the first court replied during my letters to presidents, Human Rights Watch, etc. or it was just a regular delay. The experiment purpose now seems optimistic to attain.<br />
<br />
'''28 Jun 2019'''<br />
<br />
Received a reply from Internal Affairs Ministry of Russia saying that it is not in their competence.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=351Can Human Rights Be Accomplished Experiment/Events2019-06-24T11:40:34Z<p>Victor Porton: </p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''14 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment<br />
<br />
'''24 June 2019'''<br />
<br />
Received a (delayed more than allowed by the law) reply from Kirovskiy district court of Perm city. I do not upload the reply because it contains nothing interesting except of a denial of the request and the advice to apply to a Moscow court where the Ministry of Finances is located.<br />
<br />
As I have already applied (after the delay expired illegally) to exactly the same court, I am doing nothing additional.<br />
<br />
It seems now impossible to check if the first court replied during my letters to presidents, Human Rights Watch, etc. or it was just a regular delay. The experiment purpose now seems optimistic to attain.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=350Can Human Rights Be Accomplished Experiment/Events2019-06-24T11:39:27Z<p>Victor Porton: </p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''20 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment<br />
<br />
'''24 June 2019'''<br />
<br />
Received a (delayed more than allowed by the law) reply from Kirovskiy district court of Perm city. I do not upload the reply because it contains nothing interesting except of a denial of the request and the advice to apply to a Moscow court where the Ministry of Finances is located.<br />
<br />
As I have already applied (after the delay expired illegally) to exactly the same court, I am doing nothing additional.<br />
<br />
It seems now impossible to check if the first court replied during my letters to presidents, Human Rights Watch, etc. or it was just a regular delay. The experiment purpose now seems optimistic to attain.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Motivation&diff=349Can Human Rights Be Accomplished Experiment/Motivation2019-06-23T19:09:41Z<p>Victor Porton: misc</p>
<hr />
<div>[http://portonvictor.org Victor Porton] was severely discriminated in Russia due his unusual religious and political views.<br />
<br />
Particularly, as he testifies in official documents, he suffered severe hunger and was beaten by head using a frying pan.<br />
<br />
This raised before him the following issue: If I follow the rules of my religion, I am discriminated, I cannot work, preach, do anything useful for the society. Moreover I am beaten by the head what drives me mad, and if I am mad I cannot follow the rules anyway. Among of the direct harm of brain damage, Porton was confused by the fact that brain damage makes a human mad what contradicted his concept of soul. He attempted to correct his religion, such as excluding some of less important rules, but was confused even more being unable to solve this problem.<br />
<br />
To resolve this issue, [http://books.portonvictor.org/end-of-gospel/ a new religion] appeared. The issue with brain and soul was resolved this way: A man thinks with the brain, but soul is an external backup copy of the brain.<br />
<br />
He wondered why God would allow this, especially because this prevents him to do good to the society such as mathematical research.<br />
Victor Porton decided that God made this with the following purposes:<br />
<br />
* to cause him to reject Protestantism and invent a new religion (It is somehow similar to a computer which follows a wrong algorithm and switched to another algorithm until all resources such as memory are exhausted.)<br />
* to cause legal harm, in order to be able to start the lawsuit of this experiment.<br />
<br />
So Porton decided to start this experiment of forcing the state to accept the debt arising from the harm caused.<br />
<br />
Even if this won't be accepted, Porton counts it as a success because it puts the legal system into a test and produces a "measurable" outcome, to know whether the legal system works or not.<br />
<br />
Porton estimated the harm caused by the discrimination for his scientific research as $4 trillion, and request acceptance of the full compensation not only missing professor salary. To check experimentally if gross human rights violations can be defended, Porton decided to check if the full compensation can be assigned, even despite such a request is likely to be ignored what may cause him remaining poor what could harm his mathematical and computer science research.<br />
<br />
==Theological motivation==<br />
<br />
This experiment bears similarity to:<br />
<br />
* Last Judgement (or related events)<br />
* Witnesses of the Apocalypse (however, Porton is more like a plaintiff)<br />
<br />
So Porton wants to experimentally check if they are related.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=348Can Human Rights Be Accomplished Experiment2019-06-23T19:04:59Z<p>Victor Porton: misc</p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Can rights of a person with opinions contrary to the society be accomplished?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* Is a human rights violation being gross a reason for the right not to be protected?<br />
* What has priority: legal laws or humor and shame?<br />
* Will the legal obligation to answer a legal query be accomplished if the query is completely legally correct but humorous due to the nature of described events.<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Motivation|Motivation for the research]]<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]<br />
<br />
[[Category:Humanities]]<br />
[[Category:Research in the middle]]<br />
[[Category:Law]]<br />
[[Category:Experiments]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=347Can Human Rights Be Accomplished Experiment2019-06-23T09:51:51Z<p>Victor Porton: </p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Can rights of a person with opinions contrary to the society be accomplished?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* Is a human rights violation being gross a reason for the right not to be protected?<br />
* What has priority: legal laws or humor and shame?<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Motivation|Motivation for the research]]<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]<br />
<br />
[[Category:Humanities]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Motivation&diff=346Can Human Rights Be Accomplished Experiment/Motivation2019-06-23T03:39:49Z<p>Victor Porton: </p>
<hr />
<div>[http://portonvictor.org Victor Porton] was severely discriminated in Russia due his unusual religious and political views.<br />
<br />
Particularly he suffered severe hunger and was beaten by head using a frying pan.<br />
<br />
This raised before him the following issue: If I follow the rules of my religion, I am discriminated, I cannot work, preach, do anything useful for the society. Moreover I am beaten by the head what drives me mad, and if I am mad I cannot follow the rules anyway. Among of the direct harm of brain damage, Porton was confused by the fact that brain damage makes a human mad what contradicted his concept of soul.<br />
<br />
To resolve this issue, [http://books.portonvictor.org/end-of-gospel/ a new religion] appeared. The issue with brain and soul was resolved this way: A man thinks with the brain, but soul is an external backup copy of the brain.<br />
<br />
Victor Porton decided that God made this with the following purposes:<br />
<br />
* to create a new religion (It is somehow similar to a computer which follows a wrong algorithm and switched to another algorithm until all resources such as memory are exhausted.)<br />
* to cause legal harm, in order to be able to start the lawsuit of this experiment.<br />
<br />
So Porton decided to start this experiment.<br />
<br />
Whether his rights are protected, Porton would count this experiment as a success, because it is a scientific result.<br />
<br />
Porton estimated the harm caused by the discrimination for his scientific research as $4 trillion, and request acceptance of the full compensation not only missing professor salary. To check experimentally if gross human rights violations can be defended, Porton decided to check if the full compensation can be assigned, even despite such a request is likely to be ignored what may cause him remaining poor what could harm his mathematical and computer science research.<br />
<br />
==Theological motivation==<br />
<br />
This experiment bears similarity to:<br />
<br />
* Last Judgement (or related events)<br />
* Witnesses of the Apocalypse (however, Porton is more like a plaintiff)<br />
<br />
So Porton wants to experimentally check if they are related.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=345Can Human Rights Be Accomplished Experiment/Events2019-06-23T03:32:49Z<p>Victor Porton: World Human Rights Forum</p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''20 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]<br />
<br />
'''23 June 2019'''<br />
<br />
A request with the following links sent to World Human Rights Forum:<br />
* https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/<br />
* https://en.wikiversity.org/wiki/Can_Human_Rights_Be_Accomplished_Experiment</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=344Can Human Rights Be Accomplished Experiment2019-06-23T03:26:17Z<p>Victor Porton: </p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Can rights of a person with opinions contrary to the society be accomplished?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* Is a human rights violation being gross a reason for the right not to be protected?<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Motivation|Motivation for the research]]<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]<br />
<br />
[[Category:Humanities]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Humanities&diff=343Humanities2019-06-23T03:24:39Z<p>Victor Porton: Created page with "* Can Human Rights Be Accomplished Experiment"</p>
<hr />
<div>* [[Can Human Rights Be Accomplished Experiment]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Main_Page&diff=342Main Page2019-06-23T03:24:04Z<p>Victor Porton: </p>
<hr />
<div>This is a virtual '''scientific conference'''. You can publish at this site anything you could present at a scientific meeting:<br />
<br />
* new research results;<br />
* your articles and books;<br />
* research ideas, which you could talk to colleagues verbally;<br />
* presentations, talks and videos;<br />
* curious science facts;<br />
* and even science-related jokes.<br />
<br />
The conference is currently centered on '''mathematics''', but '''all sciences''' are accepted. The topics include pure math, applied math, math in physics and other sciences, theoretical computer science.<br />
<br />
Unlike a real math conference, this virtual one runs not say every year but constantly all time.<br />
<br />
==[[Research in the middle]]==<br />
<br />
Another usage of this site is to publish research-in-the-middle: rough research ideas (such as proof ideas), negative results, incomplete calculations, etc.<br />
<br />
We will follow general ideas and conventions of [http://polymathprojects.org/ Polymath Project].<br />
<br />
However, this project is a dual of [http://polymathprojects.org/about/ Polymath project]:<br />
*Polymath is for precisely formulated problems, this wiki is not only for precise formulations but also for rough ideas.<br />
*Polymath is for problems of interest to wide variety of mathematicians, this wiki is for more special problems which may involve additional learning before joining projects presented on this site.<br />
*Polymath develops primarely on blogs and then in the wiki, this project is meant to be developed inside this wiki (don't hesitate to use blogs if you want, however).<br />
*Polymath project comes in waves focusing on particular problems. This site is to present as much problems as possible, simultaneously.<br />
This project is similar to Polymath project in the respect that these both are for massively collaborated math research.<br />
<br />
The list of our research projects is available at [[:Category:Research in the middle]]. Please participate in these projects.<br />
<br />
==Sections==<br />
<br />
* [[Mathematics]]<br />
** [[General topology]]<br />
* [[Humanities]]<br />
<br />
Feel free to create new sections you may want to place references to your research in.<br />
<br />
==About this site==<br />
<br />
When adding new research items to this site press "Signature and timestamp" button to mark that you are the author and add the time when the item was added.<br />
<br />
Should we adapt the policy that every research item is at a separate page, or should we allow several related items (by several unrelated author?) at one page? Placing every item at a separate page has the advantage that we may categorize the items by (among other categorization) author name.<br />
<br />
Currently this site is run on <code>conference.portonvictor.org</code> domain. We should get top-level domain instead. If you want to donate money for a domain, please contact [[User:Victor_Porton|Victor Porton]].<br />
<br />
To make a math formula at this site you just enclose a LaTeX formula in dollar signs: <span class="tex2jax_ignore">$E=mc^2$</span> becomes $E=mc^2$. '''Do not use <nowiki>&lt;math&gt;...&lt;/math&gt;</nowiki> tags.'''<br />
<br />
Which file formats for video lectures should we accept for uploading? (Currently we support 'pdf', 'png', 'ps', 'txt', 'doc', 'docx', 'svg', 'ppt', 'pptx'. If you want to upload another file format, contact [[User:Victor_Porton|me]].)<br />
We currently don't accept video uploads due limited space at the server. ([https://www.paypal.com/cgi-bin/webscr?cmd=_donations&business=DM6L62TFDFHN4&lc=US&item_name=Victor%20Porton%27s%20Foundation&item_number=conference&no_note=1&no_shipping=1&currency_code=USD&bn=PP%2dDonationsBF%3abtn_donateCC_LG%2egif%3aNonHosted Donate!]) Links to videos are however welcome.<br />
<br />
If any institutions wants to host this site instead of [[User:Victor_Porton|me]], please contact [[User:Victor_Porton|me]].</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Motivation&diff=341Can Human Rights Be Accomplished Experiment/Motivation2019-06-23T03:21:41Z<p>Victor Porton: typo</p>
<hr />
<div>[http://portonvictor.org Victor Porton] was severely discriminated in Russia due his unusual religious and political views.<br />
<br />
Particularly he suffered severe hunger and was beaten by head using a frying pan.<br />
<br />
This raised before him the following issue: If I follow the rules of my religion, I am discriminated, I cannot work, preach, do anything useful for the society. Moreover I am beaten by the head what drives me mad, and if I am mad I cannot follow the rules anyway. Among of the direct harm of brain damage, Porton was confused by the fact that brain damage makes a human mad what contradicted his concept of soul.<br />
<br />
To resolve this issue, [http://books.portonvictor.org/end-of-gospel/ a new religion] appeared. The issue with brain and soul was resolved this way: A man thinks with the brain, but soul is an external backup copy of the brain.<br />
<br />
Victor Porton decided that God made this with the following purposes:<br />
<br />
* to create a new religion (It is somehow similar to a computer which follows a wrong algorithm and switched to another algorithm until all resources such as memory are exhausted.)<br />
* to cause legal harm, in order to be able to start the lawsuit of this experiment.<br />
<br />
Whether his rights are protected, Porton would count this experiment as a success, because it is a scientific result.<br />
<br />
Porton estimated the harm caused by the discrimination for his scientific research as $4 trillion, and request acceptance of the full compensation not only missing professor salary. To check experimentally if gross human rights violations can be defended, Porton decided to check if the full compensation can be assigned, even despite such a request is likely to be ignored what may cause him remaining poor what could harm his mathematical and computer science research.<br />
<br />
==Theological motivation==<br />
<br />
This experiment bears similarity to:<br />
<br />
* Last Judgement (or related events)<br />
* Witnesses of the Apocalypse (however, Porton is more like a plaintiff)<br />
<br />
So Porton wants to experimentally check if they are related.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=340Can Human Rights Be Accomplished Experiment2019-06-23T03:17:59Z<p>Victor Porton: </p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Can rights of a person with opinions contrary to the society be accomplished?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* Is a human rights violation being gross a reason for the right not to be protected?<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Motivation|Motivation for the research]]<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Experiment_Conditions&diff=339Can Human Rights Be Accomplished Experiment/Experiment Conditions2019-06-23T03:13:26Z<p>Victor Porton: </p>
<hr />
<div>Legal education: none (however Porton claims some spiritual knowledge regarding law).<br />
<br />
Monthly income (as of 22 Jun 2019): ILS 6616 (USD 1849.01). (Also some unknown ILS 695.40 (USD 194.35) income appeared on the bank account.)<br />
<br />
Place of living: Ashkelon, Israel.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Experiment_Conditions&diff=338Can Human Rights Be Accomplished Experiment/Experiment Conditions2019-06-23T03:12:54Z<p>Victor Porton: Created page with "Legal education: none. Monthly income (as of 22 Jun 2019): ILS 6616 (USD 1849.01). (Also some unknown ILS 695.40 (USD 194.35) income appeared on the bank account.) Place of..."</p>
<hr />
<div>Legal education: none.<br />
<br />
Monthly income (as of 22 Jun 2019): ILS 6616 (USD 1849.01). (Also some unknown ILS 695.40 (USD 194.35) income appeared on the bank account.)<br />
<br />
Place of living: Ashkelon, Israel.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Motivation&diff=337Can Human Rights Be Accomplished Experiment/Motivation2019-06-23T03:05:51Z<p>Victor Porton: about acceptance of the full harm</p>
<hr />
<div>[http://portonvictor.org Victor Porton] was severely discriminated in Russia due his unusual religious and political views.<br />
<br />
Particularly he suffered severe hunger and was beaten by head using a frying pan.<br />
<br />
This raised before him the following issue: If I follow the rules of my religion, I am discriminated, I cannot work, preach, do anything useful for the society. Moreover I am beaten by the head what drives me mad, and if I am mad I cannot follow the rules anyway. Among of the direct harm of brain damage, Porton was confused by the fact that brain damage makes a human mad what contradicted his concept of soul.<br />
<br />
To resolve this issue, [http://books.portonvictor.org/end-of-gospel/ a new religion] appeared. The issue with brain and soul was resolved this way: A man thinks with the brain, but soul is an external backup copy of the brain.<br />
<br />
Victor Porton decided that God made this with the following purposes:<br />
<br />
* to create a new religion (It is somehow similar to a computer which follows a wrong algorithm and switched to another algorithm until all resources such as memory are exhausted.)<br />
* to cause legal harm, in order to be able to start the lawsuit of this experiment.<br />
<br />
Whether his rights are protects, Porton would count this experiment as a success, because it is a scientific result.<br />
<br />
Porton estimated the harm caused by the discrimination for his scientific research as $4 trillion, and request acceptance of the full compensation not only missing professor salary. To check experimentally if gross human rights violations can be defended, Porton decided to check if the full compensation can be assigned, even despite such a request is likely to be ignored what may cause him remaining poor what could harm his mathematical and computer science research.<br />
<br />
==Theological motivation==<br />
<br />
This experiment bears similarity to:<br />
<br />
* Last Judgement (or related events)<br />
* Witnesses of the Apocalypse (however, Porton is more like a plaintiff)<br />
<br />
So Porton wants to experimentally check if they are related.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Motivation&diff=336Can Human Rights Be Accomplished Experiment/Motivation2019-06-23T03:00:37Z<p>Victor Porton: typo</p>
<hr />
<div>[http://portonvictor.org Victor Porton] was severely discriminated in Russia due his unusual religious and political views.<br />
<br />
Particularly he suffered severe hunger and was beaten by head using a frying pan.<br />
<br />
This raised before him the following issue: If I follow the rules of my religion, I am discriminated, I cannot work, preach, do anything useful for the society. Moreover I am beaten by the head what drives me mad, and if I am mad I cannot follow the rules anyway. Among of the direct harm of brain damage, Porton was confused by the fact that brain damage makes a human mad what contradicted his concept of soul.<br />
<br />
To resolve this issue, [http://books.portonvictor.org/end-of-gospel/ a new religion] appeared. The issue with brain and soul was resolved this way: A man thinks with the brain, but soul is an external backup copy of the brain.<br />
<br />
Victor Porton decided that God made this with the following purposes:<br />
<br />
* to create a new religion (It is somehow similar to a computer which follows a wrong algorithm and switched to another algorithm until all resources such as memory are exhausted.)<br />
* to cause legal harm, in order to be able to start the lawsuit of this experiment.<br />
<br />
Whether his rights are protects, Porton would count this experiment as a success, because it is a scientific result.<br />
<br />
==Theological motivation==<br />
<br />
This experiment bears similarity to:<br />
<br />
* Last Judgement (or related events)<br />
* Witnesses of the Apocalypse (however, Porton is more like a plaintiff)<br />
<br />
So Porton wants to experimentally check if they are related.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Motivation&diff=335Can Human Rights Be Accomplished Experiment/Motivation2019-06-23T02:59:43Z<p>Victor Porton: Created page with "[http://portonvictor.org Victor Porton] was severely discriminated in Russia during his unusual religious and political views. Particularly he suffered severe hunger and was..."</p>
<hr />
<div>[http://portonvictor.org Victor Porton] was severely discriminated in Russia during his unusual religious and political views.<br />
<br />
Particularly he suffered severe hunger and was beaten by head using a frying pan.<br />
<br />
This raised before him the following issue: If I follow the rules of my religion, I am discriminated, I cannot work, preach, do anything useful for the society. Moreover I am beaten by the head what drives me mad, and if I am mad I cannot follow the rules anyway. Among of the direct harm of brain damage, Porton was confused by the fact that brain damage makes a human mad what contradicted his concept of soul.<br />
<br />
To resolve this issue, [http://books.portonvictor.org/end-of-gospel/ a new religion] appeared. The issue with brain and soul was resolved this way: A man thinks with the brain, but soul is an external backup copy of the brain.<br />
<br />
Victor Porton decided that God made this with the following purposes:<br />
<br />
* to create a new religion (It is somehow similar to a computer which follows a wrong algorithm and switched to another algorithm until all resources such as memory are exhausted.)<br />
* to cause legal harm, in order to be able to start the lawsuit of this experiment.<br />
<br />
Whether his rights are protects, Porton would count this experiment as a success, because it is a scientific result.<br />
<br />
==Theological motivation==<br />
<br />
This experiment bears similarity to:<br />
<br />
* Last Judgement (or related events)<br />
* Witnesses of the Apocalypse (however, Porton is more like a plaintiff)<br />
<br />
So Porton wants to experimentally check if they are related.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=334Can Human Rights Be Accomplished Experiment2019-06-23T02:45:50Z<p>Victor Porton: </p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Can rights of a person with opinions contrary to the society be accomplished?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* TODO<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Motivation|Motivation for the research]]<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=333Can Human Rights Be Accomplished Experiment2019-06-23T02:43:59Z<p>Victor Porton: motivation</p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* TODO<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Motivation|Motivation for the research]]<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=332Can Human Rights Be Accomplished Experiment/Events2019-06-23T02:40:54Z<p>Victor Porton: United Nations Human Rights Council request</p>
<hr />
<div>'''1 Jun 2019'''<br />
<br />
[https://portonrus.files.wordpress.com/2019/06/hrccomplaintprocedureform-discrimination.doc Request sent to United Nations Human Rights Council.]<br />
<br />
'''20 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment/Events&diff=331Can Human Rights Be Accomplished Experiment/Events2019-06-23T02:34:34Z<p>Victor Porton: Created page with "'''20 June 2019''' [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.] The request was delivered to the followi..."</p>
<hr />
<div>'''20 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ The court request sent.]<br />
<br />
The request was delivered to the following state organs:<br />
<br />
* President of Russia Vladimir Putin<br />
* Premier of Russia Dmitriy Medvedev<br />
* Foreign Affairs of Russia Ministry<br />
* Internal Affairs of Russia Ministry<br />
* President of US Donald Trump<br />
* US Department of the State<br />
* United Kingdom Premier Minister<br />
<br />
The request was also delivered to the following human rights organizations:<br />
<br />
* Human Rights Watch<br />
* European Commission<br />
* UN Watch<br />
* Human Rights First<br />
* Human Rights Foundation (note: their email did not work, I tried to contact them through Facebook)<br />
<br />
'''21 June 2019'''<br />
<br />
[https://portonmath.wordpress.com/2019/06/21/second-court-request/ Second court request sent.]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Can_Human_Rights_Be_Accomplished_Experiment&diff=330Can Human Rights Be Accomplished Experiment2019-06-23T02:23:09Z<p>Victor Porton: experiment started</p>
<hr />
<div>[http://portonvictor.org Victor Porton] conducts an experiment to check if:<br />
<br />
* Can human rights be accomplished in the modern world?<br />
* Are geniuses deprived in rights compared to common people?<br />
* Is importance of a lawsuit a factor for it not to be decided?<br />
* TODO<br />
<br />
The experiment started as described in [https://portonmath.wordpress.com/2019/06/20/a-disabled-mathematician-was-discriminated/ this blog post].<br />
<br />
* [[Can Human Rights Be Accomplished Experiment/Events|Events in chronological order]]<br />
* [[Can Human Rights Be Accomplished Experiment/Experiment Conditions|Experiment Conditions]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=General_topology&diff=119General topology2018-01-20T01:43:56Z<p>Victor Porton: error correction</p>
<hr />
<div>==Algebraic general topology==<br />
<br />
"Algebraic general topology" is the phrase used by [[User:Victor_Porton|Victor Porton]] to denote his new research in general topology, in other words theory of funcoids, reloids and their generalizations.<br />
<br />
The entire research is available online free of charge:<br />
<br />
* [http://www.mathematics21.org/binaries/present.pdf PDF slides] for easy quick introduction into Algebraic General Topology<br />
* [http://www.mathematics21.org/algebraic-general-topology.html Algebraic General Topology homepage]<br />
* [http://www.mathematics21.org/binaries/volume-1.pdf the book] (referred as "volume 1", accessible even for undergraduates)<br />
* [http://www.mathematics21.org/binaries/addons.pdf draft of things to add to volume 1 in the future]<br />
* [http://www.mathematics21.org/binaries/volume-2.pdf partial draft of volume 2] (unlike volume 1 uses more advanced prerequisites)<br />
* [http://www.mathematics21.org/binaries/ideas.pdf a list of short research ideas]<br />
* LaTeX source of the above at [https://bitbucket.org/portonv/algebraic-general-topology/overview this] and [https://github.com/vporton/algebraic-general-topology this] Git mirrors<br />
<br />
Note that manuscripts of Porton contain ''many'' new open problems. You have a work!<br />
<br />
--[[User:Victor Porton|Victor Porton]] ([[User talk:Victor Porton|talk]]) 19:16, 24 July 2016 (UTC)<br />
<br />
==On Urysohn's lemma and friends==<br />
<br />
[[User:Victor_Porton|Victor Porton]] recently has written a new proof of Urysohn's lemma. The proof is conditional (depending on [http://www.openproblemgarden.org/op/entourages_of_a_composition_of_funcoids an unsolved conjecture]) however!<br />
<br />
Currently the proof is present at http://www.mathematics21.org/binaries/addons.pdf<br />
<br />
The purpose of this new proof attempt is to find a common generalization of Urysohn's lemma and results in [http://arxiv.org/abs/1410.1504 Each regular paratopological group is completely regular] article by Taras Banakh and Alex Ravsky.<br />
<br />
--[[User:Victor Porton|Victor Porton]] ([[User talk:Victor Porton|talk]]) 19:16, 24 July 2016 (UTC)<br />
<br />
The conjecture on which it is based have been proved by me today. Now my alternative proof of Urysohn's lemma is complete. --[[User:Victor Porton|Victor Porton]] ([[User talk:Victor Porton|talk]]) 14:42, 25 December 2016 (UTC)<br />
<br />
Oh, my conjecture proof was with a serious error. --[[User:Victor Porton|Victor Porton]] ([[User talk:Victor Porton|talk]]) 16:34, 25 December 2016 (UTC)<br />
<br />
==Short notes==<br />
<br />
* [[User:Victor_Porton|Victor Porton]] has proved that "normality of a quasi-uniformity" (as defined by Taras Banakh) is determined by the quasi-proximity induced by the quasi-uniformity. --[[User:Victor Porton|Victor Porton]] ([[User talk:Victor Porton|talk]]) 19:16, 24 July 2016 (UTC)</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Failed_condition&diff=118Funcoid bases/Failed condition2017-04-18T23:24:45Z<p>Victor Porton: </p>
<hr />
<div>The following condition:<br />
<br />
4. $S$ is an upper set and $S\cap\Gamma$ is a filter on the boolean lattice $\Gamma$ (defined in the chapter "Funcoids are filters" of the book).<br />
<br />
was once thought by me to be equivalent to other three conditions. It is not so:<br />
<br />
<b>Proposition</b> 4 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
Thus in assumption of 4 we have not 3 (as otherwise both $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$<br />
and $S_1 = \operatorname{up} 1^{\mathsf{FCD}}$).</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=117Funcoid bases/Disproof2017-04-18T22:25:51Z<p>Victor Porton: punctuation typo</p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ \operatorname{up} G \mid G\in\operatorname{up}^{\Gamma} F \}$ (that is $S_1 = \bigcup_{F\in\operatorname{up}^{\Gamma} 1^{\mathsf{FCD}}} \operatorname{up} F$). Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \sqsupseteq F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \sqsupseteq<br />
F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \sqsupseteq F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n<br />
\sqsupseteq 1^{\mathsf{FCD}}$. Thus<br />
$X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n \in \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$.<br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}}\operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=116Funcoid bases/Disproof2017-04-18T22:25:08Z<p>Victor Porton: more detailed proof</p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ \operatorname{up} G \mid G\in\operatorname{up}^{\Gamma} F \}$ (that is $S_1 = \bigcup_{F\in\operatorname{up}^{\Gamma} 1^{\mathsf{FCD}}} \operatorname{up} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \sqsupseteq F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \sqsupseteq<br />
F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \sqsupseteq F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n<br />
\sqsupseteq 1^{\mathsf{FCD}}$. Thus<br />
$X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n \in \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$.<br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}}\operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=115Funcoid bases/Disproof2017-04-18T22:20:21Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ \operatorname{up} G \mid G\in\operatorname{up}^{\Gamma} F \}$ (that is $S_1 = \bigcup_{F\in\operatorname{up}^{\Gamma} 1^{\mathsf{FCD}}} \operatorname{up} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \sqsupseteq F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \sqsupseteq<br />
F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \sqsupseteq F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n<br />
\sqsupseteq 1^{\mathsf{FCD}}$. Thus<br />
$X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n \in \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$.<br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=114Funcoid bases/Disproof2017-04-18T20:44:38Z<p>Victor Porton: math typo</p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ \operatorname{up} G \mid G\in\operatorname{up}^{\Gamma} F \}$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \sqsupseteq F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \sqsupseteq<br />
F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \sqsupseteq F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n<br />
\sqsupseteq 1^{\mathsf{FCD}}$. Thus<br />
$X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n \in \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$.<br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=113Funcoid bases/Disproof2017-04-18T19:48:37Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ \operatorname{up} G \mid G\in\operatorname{up}^{\Gamma} F \}$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \sqsupseteq F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \sqsupseteq<br />
F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \sqsupseteq F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n<br />
\sqsupseteq 1^{\mathsf{FCD}}$. Thus<br />
$X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n \in \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \in S_1$.<br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=112Funcoid bases/Disproof2017-04-18T19:39:09Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ \operatorname{up} G \mid G\in\operatorname{up}^{\Gamma} F \}$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$. Thus <br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=111Funcoid bases/Disproof2017-04-18T19:38:55Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \{ up G \mid G\in\operatorname{up}^{\Gamma} F \}$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$. Thus <br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=110Funcoid bases/Disproof2017-04-18T19:28:44Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$. Thus <br />
$\operatorname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=109Funcoid bases/Disproof2017-04-18T19:28:36Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$. Thus <br />
$\operatoname{up}(X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n) \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=108Funcoid bases/Disproof2017-04-18T19:28:12Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$. Thus <br />
$X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} X_n \subseteq S_1$ as $S_1$ is an upper set.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases&diff=107Funcoid bases2017-04-18T19:25:23Z<p>Victor Porton: </p>
<hr />
<div>This page presents [[User:Victor_Porton|Victor Porton's]] conjectures about [[funcoid bases]] and related stuff as first defined in [http://www.mathematics21.org/binaries/addons.pdf this draft document].<br />
<br />
Please read [[Algebraic general topology]] book before attempt to participate in this research.<br />
<br />
The main conjecture about funcoid bases is the following:<br />
<br />
<b>Conjecture</b> The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):<br />
<br />
# $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.<br />
# $\forall X_0,\dots,X_n \in S : \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).<br />
# There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.<br />
<br />
'''$2\Rightarrow 3$ was disproved''' in [[Funcoid_bases/Disproof]].<br />
<br />
It yet remains the question whether the conditions "1" and "2" are equivalent.<br />
<br />
The below are historical materials.<br />
<br />
([[Funcoid_bases/Failed_condition|Condition "4" was shown not to be equivalent]] to the above three conditions.)<br />
<br />
$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious. It's also easy to prove that $1\Rightarrow 4$ (taking into account that $\Gamma$ is a sublattice of $\mathsf{FCD}$).<br />
<br />
$3\Rightarrow 4$ because $X,Y\in S\cap\Gamma \Rightarrow X,Y\in\Gamma\land X,Y\sqsupseteq f \Rightarrow X\sqcap Y\in\Gamma\land X\sqcap Y\sqsupseteq f \Rightarrow X\sqcap Y\in S\cap\Gamma$.<br />
<br />
Please write your research ideas at this wiki and as comments and trackbacks to [https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/ this blog post].<br />
<br />
[[Funcoid bases/Basic results]]<br />
<br />
Proposed ways to attack this conjecture:<br />
<br />
$1\Rightarrow 2$:<br />
<br />
*[[Funcoid bases/Reduce to meets of applying funcoids to ultrafilters]]<br />
<br />
$2\Rightarrow 3$:<br />
<br />
*[[Funcoid bases/Another reduce to ultrafilters]]<br />
*[[Funcoid bases/Proving existence of funcoid through lattice Gamma]]<br />
<br />
[[Category:Algebraic general topology]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=106Funcoid bases/Disproof2017-04-18T19:23:55Z<p>Victor Porton: </p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Disproof&diff=105Funcoid bases/Disproof2017-04-18T19:23:06Z<p>Victor Porton: Created page with "<b>Proposition</b> 2 does not imply 3. <b>Proof</b> Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite set) and..."</p>
<hr />
<div><b>Proposition</b> 2 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1^{\mathsf{FCD}} = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1^{\mathsf{FCD}}$<br />
are upper sets. $S_0 \neq S_1^{\mathsf{FCD}}$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1^{\mathsf{FCD}}$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
2 holds for $S_0$ because 3 implies 2.<br />
<br />
But 2 holds also for $S_1$ because:<br />
<br />
Suppose $X_0, \ldots, X_n \in S_1$. Then $X_i \in \operatorname{up}^{\Gamma} F_i$<br />
where $F_i \in S_0$. Consequently (take into account that $\Gamma$ is a<br />
sublattice of $\mathsf{FCD}$), $X_0, \ldots, X_n \in \operatorname{up}^{\Gamma}<br />
(F_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)$<br />
and so $X_0 \sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}}<br />
X_n = X_0 \sqcap \ldots \sqcap X_n \in \operatorname{up}^{\Gamma} (F_0<br />
\sqcap^{\mathsf{FCD}} \ldots \sqcap^{\mathsf{FCD}} F_n)<br />
\subseteq \operatorname{up}^{\Gamma} 1^{\mathsf{FCD}} \subseteq S_1$.<br />
<br />
3 cannot hold for both $S_0$ and $S_1$ because $\operatorname{up} f_0 = S_0$ and<br />
$\operatorname{up} f_1 = S_1$ imply $f_0 = \bigwedge^{\mathsf{FCD}} S_0 =<br />
1^{\mathsf{FCD}} = \bigwedge^{\mathsf{FCD}} S_1 = f_1$ and thus<br />
$S_0 = S_1$.</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases&diff=104Funcoid bases2017-04-18T19:21:34Z<p>Victor Porton: </p>
<hr />
<div>This page presents [[User:Victor_Porton|Victor Porton's]] conjectures about [[funcoid bases]] and related stuff as first defined in [http://www.mathematics21.org/binaries/addons.pdf this draft document].<br />
<br />
Please read [[Algebraic general topology]] book before attempt to participate in this research.<br />
<br />
The main conjecture about funcoid bases is the following:<br />
<br />
<b>Conjecture</b> The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):<br />
<br />
# $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.<br />
# $\forall X_0,\dots,X_n \in S : \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).<br />
# There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.<br />
<br />
'''$2\Rightarrow 3$ was disproved''' in [[Funcoid_bases/Disproof]].<br />
<br />
([[Funcoid_bases/Failed_condition|Condition "4" was shown not to be equivalent]] to the above three conditions.)<br />
<br />
$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious. It's also easy to prove that $1\Rightarrow 4$ (taking into account that $\Gamma$ is a sublattice of $\mathsf{FCD}$).<br />
<br />
$3\Rightarrow 4$ because $X,Y\in S\cap\Gamma \Rightarrow X,Y\in\Gamma\land X,Y\sqsupseteq f \Rightarrow X\sqcap Y\in\Gamma\land X\sqcap Y\sqsupseteq f \Rightarrow X\sqcap Y\in S\cap\Gamma$.<br />
<br />
Please write your research ideas at this wiki and as comments and trackbacks to [https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/ this blog post].<br />
<br />
[[Funcoid bases/Basic results]]<br />
<br />
Proposed ways to attack this conjecture:<br />
<br />
$1\Rightarrow 2$:<br />
<br />
*[[Funcoid bases/Reduce to meets of applying funcoids to ultrafilters]]<br />
<br />
$2\Rightarrow 3$:<br />
<br />
*[[Funcoid bases/Another reduce to ultrafilters]]<br />
*[[Funcoid bases/Proving existence of funcoid through lattice Gamma]]<br />
<br />
[[Category:Algebraic general topology]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Failed_condition&diff=103Funcoid bases/Failed condition2017-04-18T19:04:57Z<p>Victor Porton: </p>
<hr />
<div>The following condition:<br />
<br />
4. $S$ is an upper set and $S\cap\Gamma$ is a filter on the boolean lattice $\Gamma$ (defined in the chapter "Funcoids are filters" of the book).<br />
<br />
was once thought by me to be equivalent to other three conditions. It is not so:<br />
<br />
<b>Proposition</b> 4 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$ (where $1^{\mathsf{FCD}}$ signifies the diagonal of some infinite<br />
set) and $S_1^{\mathsf{FCD}} = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1^{\mathsf{FCD}}$<br />
are upper sets. $S_0 \neq S_1^{\mathsf{FCD}}$ because $1^{\mathsf{FCD}} \in S_0$ and $1^{\mathsf{FCD}} \notin S_1^{\mathsf{FCD}}$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1^{\mathsf{FCD}}$.<br />
<br />
Thus in assumption of 4 we have not 3 (as otherwise both $S_0 = \operatorname{up} 1^{\mathsf{FCD}}$<br />
and $S_1^{\mathsf{FCD}} = \operatorname{up} 1^{\mathsf{FCD}}$).</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases&diff=102Funcoid bases2017-04-18T16:11:34Z<p>Victor Porton: </p>
<hr />
<div>This page presents [[User:Victor_Porton|Victor Porton's]] conjectures about [[funcoid bases]] and related stuff as first defined in [http://www.mathematics21.org/binaries/addons.pdf this draft document].<br />
<br />
Please read [[Algebraic general topology]] book before attempt to participate in this research.<br />
<br />
The main conjecture about funcoid bases is the following:<br />
<br />
<b>Conjecture</b> The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):<br />
<br />
# $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.<br />
# $\forall X_0,\dots,X_n \in S : \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).<br />
# There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.<br />
<br />
([[Funcoid_bases/Failed_condition|Condition "4" was shown not to be equivalent]] to the above three conditions.)<br />
<br />
$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious. It's also easy to prove that $1\Rightarrow 4$ (taking into account that $\Gamma$ is a sublattice of $\mathsf{FCD}$).<br />
<br />
$3\Rightarrow 4$ because $X,Y\in S\cap\Gamma \Rightarrow X,Y\in\Gamma\land X,Y\sqsupseteq f \Rightarrow X\sqcap Y\in\Gamma\land X\sqcap Y\sqsupseteq f \Rightarrow X\sqcap Y\in S\cap\Gamma$.<br />
<br />
Please write your research ideas at this wiki and as comments and trackbacks to [https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/ this blog post].<br />
<br />
[[Funcoid bases/Basic results]]<br />
<br />
Proposed ways to attack this conjecture:<br />
<br />
$1\Rightarrow 2$:<br />
<br />
*[[Funcoid bases/Reduce to meets of applying funcoids to ultrafilters]]<br />
<br />
$2\Rightarrow 3$:<br />
<br />
*[[Funcoid bases/Another reduce to ultrafilters]]<br />
*[[Funcoid bases/Proving existence of funcoid through lattice Gamma]]<br />
<br />
[[Category:Algebraic general topology]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases&diff=101Funcoid bases2017-04-18T16:06:36Z<p>Victor Porton: </p>
<hr />
<div>This page presents [[User:Victor_Porton|Victor Porton's]] conjectures about [[funcoid bases]] and related stuff as first defined in [http://www.mathematics21.org/binaries/addons.pdf this draft document].<br />
<br />
Please read [[Algebraic general topology]] book before attempt to participate in this research.<br />
<br />
The main conjecture about funcoid bases is the following:<br />
<br />
<b>Conjecture</b> The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):<br />
<br />
# $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.<br />
# $\forall X_0,\dots,X_n \in S : \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).<br />
# There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.<br />
<br />
(Condition "4" was [[Funcoid_bases/Failed_condition|shown not to be equivalent]] to the above three conditions.)<br />
<br />
$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious. It's also easy to prove that $1\Rightarrow 4$ (taking into account that $\Gamma$ is a sublattice of $\mathsf{FCD}$).<br />
<br />
$3\Rightarrow 4$ because $X,Y\in S\cap\Gamma \Rightarrow X,Y\in\Gamma\land X,Y\sqsupseteq f \Rightarrow X\sqcap Y\in\Gamma\land X\sqcap Y\sqsupseteq f \Rightarrow X\sqcap Y\in S\cap\Gamma$.<br />
<br />
Please write your research ideas at this wiki and as comments and trackbacks to [https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/ this blog post].<br />
<br />
[[Funcoid bases/Basic results]]<br />
<br />
Proposed ways to attack this conjecture:<br />
<br />
$1\Rightarrow 2$:<br />
<br />
*[[Funcoid bases/Reduce to meets of applying funcoids to ultrafilters]]<br />
<br />
$2\Rightarrow 3$:<br />
<br />
*[[Funcoid bases/Another reduce to ultrafilters]]<br />
*[[Funcoid bases/Proving existence of funcoid through lattice Gamma]]<br />
<br />
[[Category:Algebraic general topology]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases/Failed_condition&diff=100Funcoid bases/Failed condition2017-04-18T16:05:38Z<p>Victor Porton: Created page with "The following condition: 4. $S$ is an upper set and $S\cap\Gamma$ is a filter on the boolean lattice $\Gamma$ (defined in the chapter "Funcoids are filters" of the book). wa..."</p>
<hr />
<div>The following condition:<br />
<br />
4. $S$ is an upper set and $S\cap\Gamma$ is a filter on the boolean lattice $\Gamma$ (defined in the chapter "Funcoids are filters" of the book).<br />
<br />
was once thought by me to be equivalent to other three conditions. It is not so:<br />
<br />
<b>Proposition</b> 4 does not imply 3.<br />
<br />
<b>Proof</b><br />
Take $S_0 = \operatorname{up} 1$ (where $1$ signifies the diagonal of some infinite<br />
set) and $S_1 = \bigcup_{F \in S_0} \operatorname{up}^{\Gamma} F$. Both $S_0$ and $S_1$<br />
are upper sets. $S_0 \neq S_1$ because $1 \in S_0$ and $1 \notin S_1$. The $S<br />
\cap \Gamma$ for both is the filter on $\Gamma$ defining the funcoid $1$.<br />
<br />
Thus in assumption of 4 we have not 3 (as otherwise both $S_0 = \operatorname{up} 1$<br />
and $S_1 = \operatorname{up} 1$).</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases&diff=99Funcoid bases2017-04-18T08:20:56Z<p>Victor Porton: </p>
<hr />
<div>This page presents [[User:Victor_Porton|Victor Porton's]] conjectures about [[funcoid bases]] and related stuff as first defined in [http://www.mathematics21.org/binaries/addons.pdf this draft document].<br />
<br />
Please read [[Algebraic general topology]] book before attempt to participate in this research.<br />
<br />
The main conjecture about funcoid bases is the following:<br />
<br />
<b>Conjecture</b> The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):<br />
<br />
# $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.<br />
# $\forall X_0,\dots,X_n \in S : \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).<br />
# There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.<br />
<br />
Another possibly equivalent condition:<br />
<br />
4. $S$ is an upper set and $S\cap\Gamma$ is a filter on the boolean lattice $\Gamma$ (defined in the chapter "Funcoids are filters" of the book).<br />
<br />
$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious. It's also easy to prove that $1\Rightarrow 4$ (taking into account that $\Gamma$ is a sublattice of $\mathsf{FCD}$).<br />
<br />
$3\Rightarrow 4$ because $X,Y\in S\cap\Gamma \Rightarrow X,Y\in\Gamma\land X,Y\sqsupseteq f \Rightarrow X\sqcap Y\in\Gamma\land X\sqcap Y\sqsupseteq f \Rightarrow X\sqcap Y\in S\cap\Gamma$.<br />
<br />
Please write your research ideas at this wiki and as comments and trackbacks to [https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/ this blog post].<br />
<br />
[[Funcoid bases/Basic results]]<br />
<br />
Proposed ways to attack this conjecture:<br />
<br />
$1\Rightarrow 2$:<br />
<br />
*[[Funcoid bases/Reduce to meets of applying funcoids to ultrafilters]]<br />
<br />
$2\Rightarrow 3$:<br />
<br />
*[[Funcoid bases/Another reduce to ultrafilters]]<br />
*[[Funcoid bases/Proving existence of funcoid through lattice Gamma]]<br />
<br />
[[Category:Algebraic general topology]]<br />
[[Category:Research in the middle]]</div>Victor Portonhttps://conference.portonvictor.org/w/index.php?title=Funcoid_bases&diff=98Funcoid bases2017-04-16T21:51:31Z<p>Victor Porton: </p>
<hr />
<div>This page presents [[User:Victor_Porton|Victor Porton's]] conjectures about [[funcoid bases]] and related stuff as first defined in [http://www.mathematics21.org/binaries/addons.pdf this draft document].<br />
<br />
Please read [[Algebraic general topology]] book before attempt to participate in this research.<br />
<br />
The main conjecture about funcoid bases is the following:<br />
<br />
<b>Conjecture</b> The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):<br />
<br />
# $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.<br />
# $\forall X_0,\dots,X_n \in S : \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).<br />
# There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.<br />
<br />
Another possibly equivalent condition:<br />
<br />
4. $S$ is an upper set and $S\cap\Gamma$ is a filter on the boolean lattice $\Gamma$ (defined in the chapter "Funcoids are filters" of the book).<br />
<br />
$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious. It's also easy to prove that $1\Rightarrow 4$ (taking into account that $\Gamma$ is a closed sublattice of $\mathsf{FCD}$).<br />
<br />
$3\Rightarrow 4$ because $X,Y\in S\cap\Gamma \Rightarrow X,Y\in\Gamma\land X,Y\sqsupseteq f \Rightarrow X\sqcap Y\in\Gamma\land X\sqcap Y\sqsupseteq f \Rightarrow X\sqcap Y\in S\cap\Gamma$.<br />
<br />
Please write your research ideas at this wiki and as comments and trackbacks to [https://portonmath.wordpress.com/2017/04/11/research-in-the-middle-project/ this blog post].<br />
<br />
[[Funcoid bases/Basic results]]<br />
<br />
Proposed ways to attack this conjecture:<br />
<br />
$1\Rightarrow 2$:<br />
<br />
*[[Funcoid bases/Reduce to meets of applying funcoids to ultrafilters]]<br />
<br />
$2\Rightarrow 3$:<br />
<br />
*[[Funcoid bases/Another reduce to ultrafilters]]<br />
*[[Funcoid bases/Proving existence of funcoid through lattice Gamma]]<br />
<br />
[[Category:Algebraic general topology]]<br />
[[Category:Research in the middle]]</div>Victor Porton