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.
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 […]
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.
“Upgrading a Multifuncoid” article upgraded
Now my article Upgrading a Multifuncoid is updated. The main change is that it now contains the conjecture “Upgrading a completary multifuncoid is a completary multifuncoid” (see the article for an exact formulation).
Product of two funcoids and product of two funcoids
I’ve put online an article (PDF, a partial draft) where I define product of two morphisms for certain categories. (Such products are pointfree funcoids.) Particularly it is defined product of two funcoids and product of two reloids. It is a more mature version of a draft I put online previously.