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 […]
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 […]
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 […]
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 […]
Two new chapters in my math draft
I’ve added chapters “Cartesian closedness” and “Singularities” (from the site http://tiddlyspace.com which will be closed soon) to volume 2 draft. Both chapters are very rough draft and present not rigorous proofs but rough ideas.
A negative result on a conjecture
Due my research about singularities the problem formulated in this blog post was solved negatively with help of Alex Ravsky who has found a counter-example. The conjecture was: $latex \mathrm{GR}(\Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections. The counter-example follows: $latex f=\{(x,y)\in\mathbb R^2:|x|\le |y| \vee y=0\}$, $latex g=\{(x,y)\in\mathbb R^2:|x|\ge |y| \vee x=0\}$. It is easy […]
A suggested way to solve an open problem
On the task formulated in this blog post: An attempt to prove that $latex \mathrm{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections (see http://portonmath.tiddlyspace.com/#[[Singularities%20funcoids%3A%20some%20special%20cases]]) http://portonmath.tiddlyspace.com/#[[Singularities%20funcoids%3A%20special%20cases%20proof%20attempts]]
A wiki about applying generalized limit to singularities theory
I have created a wiki about development of theory of singularities using generalized limits. Please read my book (where among other I define generalized limits) and then participate in this research wiki. Study singularities in this novel approach and share Nobel Prize with me!
A mathematical theory of singularities!
I present my mathematical theory of singularities. It may probably have applications in general relativity and other physics. The definitions are presented in this short draft article. Before reading this article I recommend to skim through my research monograph (in the field of general topology), because the above mentioned article uses concepts defined in my […]
Rough idea: Operations on singularities and their application to general relativity
I discovered a math theory which (among other things) gives an alternate interpretation of the equations of general relativity (something like to replacing real numbers with complex numbers in a quadratic equation). This theory is a theory of limits in points of singularities and properties of singularities based on my theory of funcoids (a new […]