An infinitely big structure in the center of a black hole?
I remind that I defined generalized limit of arbitrary function. The limit may be an infinitely big value. It allows to define derivative and integral of an arbitrary function. I also defined what are solutions of partial differential equations where such infinities (instead of e.g. real numbers or complex numbers) are defined. You may see […]
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 […]
Algebraic General Topology – A Game Changing Mathematical Theory
This new research field generalizes new theorems as well as former analysis by collapsing several theorems of analysis into one AGT equation:
Infinitesimal Calculus on the Reverse in my Book “Limit of a Discontinuous Function”
Traditional calculus as first considered in 17th century by Isaac Newton (and Leibniz, however some say Leibniz stole the Newton’s idea) and then 150 years later formalized (formulated correctly) by Cauchy and Weierstrass, uses limits. Initially calculus was called “infinitesimal calculus”, but in recent time the collocation “infinitesimal calculus” is usually used for a more […]
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 […]