My article has been accepted for publication
Today I’ve received email saying that my article “Funcoids and Reloids: a Generalization of Proximities and Uniformities” has been accepted for publication in European Journal of Pure and Applied Mathematics. See also the preprint of this article.
My conjecture partially solved
I’ve partially solved my conjecture, proposed Polymath problem described at this page. The problem asks which of certain four expressions about filters on a set are always pairwise equal. I have proved that the first three of them are equal, equality with the fourth remains an open problem. For the (partial) solution see this online […]
A new section in my research monograph
I added the definition and properties of “second reloidal product” (the definition was inspired by Tychonoff product of topological spaces) to my research monograph “Algebraic General Topology. Volume 1”. See the subsection “Second reloidal product” in the section “Multireloids”.
“Algebraic General Topology. Volume 1” checked for errors
I have finished checking my book “Algebraic General Topology. Volume 1” for errors. That said some minor errors may yet remain, probably I will check it again. At the time of writing this blog post the book is available online. Enjoy this new theory.
Fake alarm: There was no error in my book
I’ve sent my book (Algebraic General Topology. Volume 1) to a publisher. Afterward I’ve withdrawn it due an error. This was a fake alarm: I’ve found an error where there was no error. Today I’ve submitted it to the publisher again. Now (before copyright transfer) the book is available online.
My book “Algebraic General Topology. Volume 1” has a serious error
I found a serious error in my book. The error is in the proof of the lemma currently numbered 15.140. I for now was unable to write a correct proof of this lemma (nor of some appropriate weakening of this lemma). So I’ve withdrawn the book from the publisher.
My math book sent to a competition
I have sent my book “Algebraic General Topology. Volume 1” to EMS Monograph Award competition, which provides a 10000 EUR prize for best math research monograph. I hope to win the prize and also to publish my book with EMS. While the copyright is not yet transferred to a publisher, you may read my draft […]
“Algebraic General Topology. Volume 1” – now entire my theory here
The current draft (PDF) of the book “Algebraic General Topology. Volume 1” contains the entire general topology theory which I’ve discovered (so called Algebraic General Topology). Now is a happy day when my entire theory is put into one PDF file (190 A4 pages). In this version of the book are however missing an introductory […]
Funcoids and reloids in my math book draft
My partial draft book now contains the theory of funcoids and reloids. You may use this online draft (while I have not yet transferred the copyright) to study my theory of funcoids and reloids. Pointfree funcoids, multidimensional funcoids and staroids presented in my articles are not yet added to this partial draft.
“Algebraic General Topology. Volume 1”. Filters section finished
I have finished writing (but not yet editing and catching errors) of the section “Filters and Filtrators” of my book Algebraic General Topology. Volume 1. Now it is 63 A4 pages. Download it before I transfer copyright to EMS. Please use this my partial book for your deep study on the topic of filters on […]