Candidate formulas for product of reloids
First, we can define product of reloids as a trivial generalization of the alternative definition of product of uniform spaces. There are no trivial simplification of this relatively inelegant definition, it is not algebraic as I would want. I (without any evidence or intuition) propose two open questions one of which may be true despite […]
The end of Algebraic General Topology?
It was my long time dream since the first course of the university to do math analysis in algebraic fashion instead of the notorious epsilon-delta notation overloaded with quantifiers. This dream has been accomplished. I discovered a new math theory in which I call Algebraic General Topology in the field of General Topology. It all […]
“Upgrading multifuncoid” conjecture proved
I have proved the conjecture “Upgrading a multifuncoid is multifuncoid”. The proof is currently presented in this online draft article.
The article about ordinal numbers and product
I’ve sent this article to an open access peer reviewed journal: A New Kind of Product of Ordinal Number of Relations having Ordinal Numbers of Arguments (the article is available online).
An article about functions taking ordinal number of arguments
I’ve put online this article. It is a rough draft, is incomplete and contains little errors. Nevertheless I hope you’ll enjoy reading it: A New Kind of Product of Ordinal Number of Relations having Ordinal Numbers of Arguments
Circuitoids, a Generalization of Categories
Circuitoids are a generalization of a category where each morphisms has an arbitrary (possibly infinite) number of arguments. Two morphisms are not required to have the same number of arguments. See this manuscript where I first define circuitoids. I haven’t (yet) defined some notion of associativity for circuitoids. This may be a topic of our […]
A proposal for arXiv – managing patches
A famous mathematician Gowers wrote that it is needed “a positive strategy of actually setting up a new system might work rather better” for publishing math articles. In this post I suggest a way for the community to improve quality of self-published (or self-archived as scientists say) articles. I suggest to add the following feature […]
On product of an arbitrary family of funcoids
I previously defined product of two funcoids. Now the description of product of two funcoids is integrated into my article about multifuncoids. In this article I now also define product of an arbitrary (possibly infinite) family of multifuncoids. The article is yet a very rough preliminary partial draft. The relations of my definition of product […]
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 […]
A draft about multifuncoids
I put online a rough preliminary draft about multifuncoids, a generalization of funcoids. It contains a few definitions, and theorems. Probably the most interesting thing in it is what I call graph-composition of multifuncoids. The draft contains several open problems.