A conjecture about direct product of funcoids
I am attempting to define direct products in the category cont(mepfFcd) (the category of monovalued, entirely defined continuous pointfree funcoids), see this draft article for a definition of this category. A direct product of objects may possibly be defined as the cross-composition product (see this article). A candidate for product of morphisms $latex f_1:\mathfrak{A}\rightarrow\mathfrak{B}$ and […]
Is every isomorphisms of the category of funcoids a discrete funcoid?
The following is an important question related with categories related with funcoids: Question Is every isomorphisms of the category of funcoids a discrete funcoid?
I’ve solved two yesterday problems, one yet remains unsolved
I have solved the first two of these three open problems I proposed, but have no clue how to solve the third. (Actually, I’ve solved only a special case of the second problem, but that’s OK, this special case is enough for all practical needs.) The solutions are in this article. I asked about the […]
Three new conjectures
See here (especially this draft article) for definition of cross-composition product and quasi-cartesian functions. Conjecture 1 Cross-composition product (for small indexed families of relations) is a quasi-cartesian function (with injective aggregation) from the quasi-cartesian situation $latex {\mathfrak{S}_0}&fg=000000$ of binary relations to the quasi-cartesian situation $latex {\mathfrak{S}_1}&fg=000000$ of pointfree funcoids over posets with least elements. Conjecture […]
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 […]
“Upgrading multifuncoid” conjecture proved
I have proved the conjecture “Upgrading a multifuncoid is multifuncoid”. The proof is currently presented in this online draft article.
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.
“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).