I’ve sent the final version of the first edition of my research monograph Algebraic General Topology. Volume 1 to Russian publisher INFRA-M and signed the publication contract. They are going to publish my book electronically. They also asked to send them a…

read morePlease 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.

read moreI have rewritten the section “More results on restricted identities” of this draft. Now it contains some new (easy but important) formulas.

read moreI 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…

read moreI removed from my draft sections about “categories under Rel”. The removal happened because I developed a more general and more beautiful theory. The old version is preserved in Git history.

read moreI announced that I have introduces axioms for “restricted identities”, a structure on a category which allows to turn the category into a semigroup (abstracting away objects). But I noticed that these axioms do not fit into concrete examples which I am…

read moreIn this draft (to be moved into the online book in the future, but the draft is nearing finishing this topic, not including functors between categories with restricted identities) I described axioms and properties of categories with restricted identities. Basically, a category…

read moreI 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…

read moreI added a few new propositions into “Equivalent filters and rebase of filters” section (now located in the chapter “Filters and filtrators”) of my book. I also define “unfixed filters” as the equivalence classes of (small) filters on sets. This is a…

read moreI’ve added a new section “Double filtrators” to the bookÂ “Algebraic General Topology. Volume 1”. I show that it’s possible to describe $latex (\mathsf{FCD})$, $latex (\mathsf{RLD})_{\mathrm{out}}$, and $latex (\mathsf{RLD})_{\mathrm{in}}$ entirely in terms of filtrators (order). This seems not to lead to really interesting…

read more