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, […]
New math research wiki
I’ve created a new wiki site for math research. The motto of this wiki is “a research in the middle”. The site is intended to discuss research ideas, aspiring ways of research, usage of open problems and ways to prove open problems, etc. The exact rules are not yet defined, but I published several example […]
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 […]
“Categories related with funcoids”, a new draft
I started to write a new article Categories related with funcoids. It is now a very preliminary partial draft.
Category without the requirement of Hom-sets to be disjoint
From this Math.SE post: It would be helpful to have a standard term XXX for “a category without the requirement of Hom-sets to be disjoint” and “category got from XXX by adding source and destination object to every morphism”. This would greatly help to simplify at least 50% of routine definitions of particular categories. Why […]
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?
Error corrected
In my draft article Multifuncoids there was a serious error. I defined funcoidal product wrongly. Now a new version of the article (with corrected error) is online.
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 […]
Abrupt categories induced by categories with star-morphisms
In this blog post I introduced the notion of category with star-morphisms, a generalization of categories which have aroused in my research. Each star category gives rise to a category (abrupt category, see a remark below why I call it “abrupt”), as described below. Below for simplicity I assume that the set $latex {M}&fg=000000$ and […]