A breakthrough and getting stuck
I had a very great idea in the field of general topology, what I now call funcoids. Years of my research of funcoids culminated me writing a research monograph about funcoids and related stuff. But after I’ve finished this monograph and submitted it to a publisher, I realize that I get stuck. I have no […]
A new section in my research monograph
I added the definition and properties of “second reloidal product” (the definition was inspired by Tychonoff product of topological spaces) to my research monograph “Algebraic General Topology. Volume 1”. See the subsection “Second reloidal product” in the section “Multireloids”.
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 […]
A new simple proposition about generalized limits
I’ve added the following almost trivial proposition to the draft of my book “Algebraic General Topology. Volume 1”: Proposition $latex \tau \left( y \right) = \mathrm{xlim}\, \left( \left\langle \mu \right\rangle^{\ast} \left\{ x \right\} \times^{\mathsf{FCD}} \uparrow^{\mathrm{Base}\, \left( \mathrm{dom}\, \nu \right)} \left\{ y \right\} \right)$ (for every $latex x$). Informally: Every $latex \tau \left( y \right)$ is […]
Meta-singular numbers
I’ve defined (well, vaguely defined) what I call “meta-singular numbers”. These can be used to describe values of a function in a singularity. See this PlanetMath article.
“Algebraic General Topology. Volume 1” checked for errors
I have finished checking my book “Algebraic General Topology. Volume 1” for errors. That said some minor errors may yet remain, probably I will check it again. At the time of writing this blog post the book is available online. Enjoy this new theory.
Fake alarm: There was no error in my book
I’ve sent my book (Algebraic General Topology. Volume 1) to a publisher. Afterward I’ve withdrawn it due an error. This was a fake alarm: I’ve found an error where there was no error. Today I’ve submitted it to the publisher again. Now (before copyright transfer) the book is available online.
Welcome to collaborative research on PlanetMath.org
Background information: I’ve written a math book and submitted it to a publisher. But afterward I found a serious error (a wrong proof of the conjecture below) and have withdrawn it from the publisher. Now the draft book is available online. (You will enjoy reading it if you are interested in general topology.) I welcome […]
My book “Algebraic General Topology. Volume 1” has a serious error
I found a serious error in my book. The error is in the proof of the lemma currently numbered 15.140. I for now was unable to write a correct proof of this lemma (nor of some appropriate weakening of this lemma). So I’ve withdrawn the book from the publisher.
Toward formalization of partial infima and suprema
I’ve written a short note about suprema and infima in formal math: Toward formalization of partial infima and suprema It is especially useful for these who do math formally (in proof assistants), but may be inspiring for regular mathematicians too.