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…

read moreI’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…

read moreAbstract. 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 moreAlgebraic general topology – what is it? First, what is a general topology? General topology is the theory of topological spaces, as well as uniform spaces, proximity spaces, and metric spaces. I made a rather big discovery – a general theory that…

read moreThis new research field generalizes new theorems as well as former analysis by collapsing several theorems of analysis into one AGT equation:

read moreTraditional 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…

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,…

read moreContinuing 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…

read moreA 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 $latex f$…

read moreAlgebraic 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…

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