I’ve published a new edition of my book Algebraic General Topology. The new edition features “unfixed morphisms” a way to turn a category into a semigroup. (Certain additional structure on the category is needed.) The book features a wide generalization of general…
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Abstract. A review of my book “Generalized limit (of arbitrary discontinuous function)”. A popular introduction with graphs to the following topic: I consider (a generalized) limit of an arbitrary (discontinuous) function, defined in terms of funcoids. The definition of the generalized limit…
read moreContinuing my research from general topology monograph Algebraic General Topology, the following new open problems arose: I remind that I define generalized limit of arbitrary function. This limit is defined in terms of funcoids. As I show in the Book 3, Algebra,…
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Algebraic general topology Filters General Topology Math on the Web Nonsmooth analysis Pointfree topology Publications
Algebraic General Topology (a book series for both postdoctorals and college students) is a new branch of mathematics that replaces General Topology. Yes, general topology is now legacy! We have something better than topological spaces, funcoids. You almost spent time in vain…
read moreAfter 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…
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Algebraic general topology Filters General Topology Life Math on the Web Nonsmooth analysis Open problems Pointfree topology Publications
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 moreThe online book Algebraic General Topology. Volume 1 was updated. The update corrects a few errors in the section “Equivalent filters and rebase of filters” (which was previously marked as unchecked for errors).
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.
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