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Difference between revisions of "Funcoid bases"

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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].
 
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].
  
Please read [[Algebraic general topology]] before attempt to participate in this research.
+
Please read [[Algebraic general topology]] book before attempt to participate in this research.
  
 
The main conjecture about funcoid bases is the following:
 
The main conjecture about funcoid bases is the following:

Revision as of 09:05, 13 April 2017

This page presents Victor Porton's conjectures about funcoid bases and related stuff as first defined in this draft document.

Please read Algebraic general topology book before attempt to participate in this research.

The main conjecture about funcoid bases is the following:

Conjecture The following are equivalent (for every lattice $\mathsf{FCD}$ of funcoids between some sets and a set $S$ of principal funcoids (=binary relations)):

  1. $\forall X, Y \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S$.
  2. $\forall X_0,\dots,X_n \in S : \operatorname{up} (X \sqcap^{\mathsf{FCD}} \dots \sqcap^{\mathsf{FCD}} X_n) \subseteq S$ (for every natural $n$).
  3. There exists a funcoid $f\in\mathsf{FCD}$ such that $S=\operatorname{up} f$.

$3\Rightarrow 2$ and $2\Rightarrow 1$ are obvious.

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Proposed ways to attack this conjecture:

$1\Rightarrow 2$:

$2\Rightarrow 3$: