Categories with star-morphisms, a generalization of categories
In my research aroused a new kind of structures which I call categories with star-morphisms. In this blog post I define categories with star-morphisms. For sample usages of star categories see this draft article. Definition 1 A pre-category with star-morphisms consists of a pre-category $latex {C}&fg=000000$ (the base pre-category); a set $latex {M}&fg=000000$ (star-morphisms); a […]
Multidimensional Funcoids – draft available
The status of the article “Multidimensional Funcoids” is raised from “very rough partial draft” to “rough partial draft”. It means that now you probably can understand this my writing. See my research in general topology.
A difficulty on the way of my research
The following conjecture seems trivial but I have a hard hour trying to prove it. I suspect I have a big difficulty on the course of my research. Conjecture $latex \prod^{\mathsf{FCD}} a \not\asymp\prod^{\mathsf{FCD}} b \Leftrightarrow \forall i\in n : a_i \not\asymp b_i$ for every $latex n$-indexed (where $latex n$ is an arbitrary index set) families […]
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 […]