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Normality of a quasi-uniform space on a topology is determined by the proximity induced by the quasi-uniform space
First a prelude: Taras Banakh, Alex Ravsky “Each regular paratopological group is completely regular” solved a 60 year old open problem. Taras Banakh introduces what he call normal uniformities (don’t confuse with normal topologies). My new result, proved with advanced funcoids theory (and never tried to prove it with basic general topology): Whether a uniformity on […]
Virtual mathematics conferences opened!
I have just created a new wiki Web site, which is a virtual math conference, just like a real math meeting but running all the time (not say once per two years). https://conference.portonvictor.org Please spread the word that we have a new kind of math conference. Please post references to your articles, videos, slides, etc.
Normal quasi-uniformity elegantly defined
Error in the proof of below theorem!! http://www.math.portonvictor.org/binaries/addons.pdf My earlier attempt to describe normal reloids (where the normality is taken from “Each regular paratopological group is completely regular” article, not from the customary normality of the induced topological space) failed. After a little more thought, I have however proved (see addons.pdf) a cute algebraic description […]
About “Each regular paratopological group is completely regular” article
In this blog post I consider my attempt to rewrite the article “Each regular paratopological group is completely regular” by Taras Banakh, Alex Ravsky in a more abstract way using my theory of reloids and funcoids. The following is a general comment about reloids and funcoids as defined in my book. If you don’t understand […]
My math research monograph updated
I have uploaded a new version of my research monograph in general topology. It weakens conditions of some theorems in “Pointfree funcoids” section (thus making theorems more general), restructures the text and contain other small changes. The book download is freely available.
My book was checked for errors
I have checked for errors the entire text of my research monograph Algebraic General Topology. Volume 1 in which I generalize basic concepts of general topology using so called “funcoids” instead of topological spaces. Enjoy reading this prominent math research.
My book is now available free of charge
Today I’ve took the bold decision to put my math research book online free (under Creative Commons license), with LaTeX source available for editing by anyone at a Git hosting. Because of conflict of licensing, it seems not that my book will be never published officially. However publishing in Git has some advantages: If I […]
Modular hyperlinked mathematics (as a replacement of books)
The following are suggestions how to replace math books with hyperlinked modules, in general, and particularly suggestions how to support it in a future version of TeXmacs software. TeXmacs is an advanced math writing software, and the easiest way to implement my ideas are to modify this existing software, rather than writing a completely new […]
Todd Trimble’s commentary on my math research
Todd Trimble has notified me that he has written a “commentary” (notes) on my theory of funcoids presented in my monograph. His commentary is available at this nLab wiki page. I’ve started to read his notes. First I needed to lookup into Wikipedia to know what Chu space is. He uses category theory however as […]