# General topology

## Algebraic general topology

"Algebraic general topology" is the phrase used by Victor Porton to denote his new research in general topology, in other words theory of funcoids, reloids and their generalizations.

The entire research is available online free of charge:

- PDF slides for easy quick introduction into Algebraic General Topology
- Algebraic General Topology homepage
- the book (referred as "volume 1", accessible even for undergraduates)
- draft of things to add to volume 1 in the future
- partial draft of volume 2 (unlike volume 1 uses more advanced prerequisites)
- a list of short research ideas
- LaTeX source of the above at this and this Git mirrors

Note that manuscripts of Porton contain *many* new open problems. You have a work!

--Victor Porton (talk) 19:16, 24 July 2016 (UTC)

## On Urysohn's lemma and friends

Victor Porton recently has written a new proof of Urysohn's lemma. The proof is conditional (depending on an unsolved conjecture) however!

Currently the proof is present at http://www.mathematics21.org/binaries/addons.pdf

The purpose of this new proof attempt is to find a common generalization of Urysohn's lemma and results in Each regular paratopological group is completely regular article by Taras Banakh and Alex Ravsky.

--Victor Porton (talk) 19:16, 24 July 2016 (UTC)

The conjecture on which it is based have been proved by me today. Now my alternative proof of Urysohn's lemma is complete. --Victor Porton (talk) 14:42, 25 December 2016 (UTC)

Oh, my conjecture proof was with a serious error. --Victor Porton (talk) 16:34, 25 December 2016 (UTC)

## Short notes

- 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. --Victor Porton (talk) 19:16, 24 July 2016 (UTC)