Category: General Topology

The book “Algebraic General Topology” published officially

After a long time of being an unaccepted genius, the first volume of my book Algebraic General Topology is published officially (by the biggest Russian science publisher INFRA-M). The most general in general topology and algebraic theory, generalization of limit for multivalued discontinuous functions, algebraic formula of continuity (for multivalued functions), common theory of calculus […]

Monograph “Algebraic General Topology. Volume 1” sent for publication

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 Russian translation of my book to publish both in print and electronically. The […]

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 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 […]

Removed some sections from my draft

I 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.

Restricted identity axioms changed

I 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 going to research. So I have rewritten the text about restricted identities with […]

Categories with restricted identities

In 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 with restricted identities is a category $latex \mathcal{C}$ together with morphisms $latex \mathrm{id}^{\mathcal{C}(A,B)}_X$ […]

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 […]

Rebase of filters and equivalent filters

I 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 step forward to also define “unfixed funcoids” and “unfixed reloids”.