A new theorem about subatimic product
I recently discovered what I call subatomic product of funcoids. Today I proved a simple theorem about subatomic product: Theorem $latex \prod^{\left( A \right)}_{i \in n} \left( g_i \circ f_i \right) = \prod^{\left( A \right)} g \circ \prod^{\left( A \right)} f$ for indexed (by an index set $latex n$) families $latex f$ and $latex g$ […]
Subatomic products – a new kind of product of funcoids
I’ve discovered a new kind of product of funcoids, which I call subatomic product. Definition Let $latex f : A_0 \rightarrow A_1$ and $latex g : B_0 \rightarrow B_1$ are funcoids. Then $latex f \times^{\left( A \right)} g$ (subatomic product) is a funcoid $latex A_0 \times B_0 \rightarrow A_1 \times B_1$ such that for every […]
Errata for Filters on Posets and Generalizations
I’ve uploaded a little errata for Filters on Posets and Generalizations article published in IJPAM.
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.