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 […]
Every Pointfree Funcoid on a Semilattice is an Algebraic Structure
Continuing this blog post: The set of all pointfree funcoids on upper semilattices with least elements is exactly a certain algebraic structure defined by propositional formulas. Really just add the identities defining a pointfree funcoid to the identities of an upper semilattice with least element. I will list the exact list of identities defining a […]
Funcoid is a “Structure” in the Sense of Math Logic
A few seconds ago I realized that certain cases of pointfree funcoids can be described as a structure in the sense of mathematical logic, that is as a finite set of operations and relational symbols. Precisely, if a pointfree funcoid $latex f$ is defined on a lattice (or semilattice) with a least element $latex \bot$, […]
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 […]
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.
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 […]
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 […]
Double filtrators (new book section)
I’ve added a new section “Double filtrators” to the book “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 results but it’s curious.