Please nominate me for Doob Prize in mathematics
Please nominate my math research book (can be easily read by every mathematician) for Doob Prize. All necessary information can be found at this page at Terry Tao’s blog and subcomments. And yes, my book is worth prize.
New results about categories with restricted identities
I have rewritten the section “More results on restricted identities” of this draft. Now it contains some new (easy but important) formulas.
New concept in category theory: “unfixed morphisms”
I have developed my little addition to category theory, definition and research of properties of unfixed morphisms. Unfixed morphisms is a tool for turning a category (with certain extra structure) into a semigroup, that is abstracting away objects. Currently this research is available in this draft. I am going to rewrite my online book using […]
Math volunteer job
I welcome you to the following math research volunteer job: Participate in writing my math research book (volumes 1 and 2), a groundbreaking general topology research published in the form of a freely downloadable book: implement existing ideas, propose new ideas develop new theories solve open problems write and rewrite the book and other files […]
Error in my book
There is an error in recently added section “Equivalent filters and rebase of filters” of my math book. I uploaded a new version of the book with red font error notice. The error seems not to be serious, however. I think all this can be corrected. Other sections of the book are not affected at […]
My math book updated
I have updated my math book with new (easy but) general theorem similar to this (but in other notation): Theorem If $latex \mathfrak{Z}$ is an ideal base, then the set of filters on $latex \mathfrak{Z}$ is a join-semilattice and the binary join of filters is described by the formula $latex \mathcal{A}\sqcup\mathcal{B} = \mathcal{A}\cap\mathcal{B}$. I have updated some […]
My math book updated
I updated my math research book to use “weakly down-aligned” and “weakly up-aligned” instead of “down-aligned” and “up-aligned” (see the book for the definitions) where appropriate to make theorems slightly more general. During this I also corrected an error. (One theorem referred to complement of a lattice element without stating that the lattice is boolean.) Well, maybe I […]
Peer review for open access math books
We have a new kind of math publishing: Free books distributed through Internet. It is a new kind of mathematical culture. Some books of this kind appeared with daunting success. It has great advantages. It is how things should be done in modern times. But it miss an essential part of math tradition, peer review. For […]
My article is ignored
The journal European Journal of Pure and Applied Mathematics has accepted my article after a peer review and asked me to send it in their LaTeX format. I had a hyperref trouble with my LaTeX file. So I’ve said them that I withdraw my article. But later I realized that the best thing I can […]
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 […]