New Edition of the Book “Algebraic General Topology. Book 1: Basics”
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 topology done in an algebraic way. Now we can operate on general topological […]
A Popular Introduction into the Generalized Limit (of arbitrary discontinuous function)
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 makes it obvious to define such things as the derivative of an arbitrary […]
Some Conjectures About Generalized Limits
Continuing 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, generalized limit is defined for generalized spaces, for example for reloids. So, how […]
Algebraic General Topology, a New Branch of Mathematics (Book) and How It Is Related With Limit of Discontinuous Function
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 studying topological spaces: In not so far future colleges will teach funcoids courses […]
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 […]
Algebraic General Topology. Volume 1 updated
The 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).
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 […]
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.