“Algebraic General Topology. Volume 1”. Filters section finished
I have finished writing (but not yet editing and catching errors) of the section “Filters and Filtrators” of my book Algebraic General Topology. Volume 1. Now it is 63 A4 pages. Download it before I transfer copyright to EMS. Please use this my partial book for your deep study on the topic of filters on […]
Errata for Filters on Posets and Generalizations
I’ve uploaded a little errata for Filters on Posets and Generalizations article published in IJPAM.
How to teach filters to young mathematicians
I propose the following way to introduce filters on sets to beginning students. (I am writing a book which contains this intro now.) You are welcomed to comment whether this is a good exposition and how to make it even better. We sometimes want to define something resembling an infinitely small (or infinitely big) set, […]
Polymath problem: Difference of two filters
My open problem first published in this my blog post (about pair-wise equality of four different expressions for differences of two filters) may be considered to be the next polymath problem. Well, I realize that this may problem may be not ideal for polymath, because to approach a solution of this problem not inventing my […]
My first article is published
My first math article (titled “Filters on Posets and Generalizations”) was recently published in a peer reviewed, open access journal. Why I published my first research article only in the age of 31? See my short autobiography.
Orderings of filters in terms of reloids, draft
I updated the article Orderings of filters in terms of reloids from “preliminary draft” to just “draft”. It means most errors are corrected and now you can read it.
Conjecture: Upgrading a multifuncoid
This short article is the first my public writing where I introduce the concept of multidimensional funcoid which I am investigating now. But the main purpose of this article is to formulate a conjecture (see below). This is the shortest possible writing enough to explain my conjecture to every mathematician. Refer to this Web site […]
My research is stalled
My research of n-ary funcoids is stalled now, as I am (yet) unable to solve certain problem. I posted a special version of this problem to MathOverflow. Please help me to solve this open problem. It is a very important problem.
I submit theory of filters to IJPAM
I previously submitted my article about filters on posets to Armenian Journal of Mathematics. I waited for review of my article about 17 months and they haven’t replied. So I withdraw my submission and now am submitting to an other journal, International Journal of Pure and Applied Mathematics.
Oblique product of filters
Funcoids and reloids are my research in the field of general topology. Let $latex \mathcal{A}$ and $latex \mathcal{B}$ are filters. Earlier I introduced three kinds of products of filters: funcoidal product: $latex \mathcal{A}\times^{\mathsf{FCD}}\mathcal{B}$; reloidal product: $latex \mathcal{A}\times^{\mathsf{RLD}}\mathcal{B}$; second product: $latex \mathcal{A}\times^{\mathsf{RLD}}_F\mathcal{B}$; The last two products are reloids while the first is a funcoid. Funcoidal and […]