“Algebraic General Topology. Volume 1”. Filters section finished
I have finished writing (but not yet editing and catching errors) of the section “Filters and Filtrators” of my book Algebraic General Topology. Volume 1. Now it is 63 A4 pages. Download it before I transfer copyright to EMS. Please use this my partial book for your deep study on the topic of filters on […]
A readable draft of “Multidimensional Funcoids”
I created a new draft of my article Multidimensional Funcoids article, which is probably has become readable now. Nevertheless there may be many errors yet. Now I am going to concentrate my efforts into putting my research in a book form for participating in EMS Monograph Award.
A change in terminology: multifuncoid -> staroid
I’ve made a change in terminology in my draft article Multidimensional funcoids: multifuncoid → staroid. I now use the term “multifuncoid” in an other sense. I made the change of the terminology in order for the meaning of the term “multifuncoid” to become more similar to the meaning of the term “pointfree funcoid”.
A conjecture related with subatomic product
With subatomic products first mentioned here and described in this article are related the following conjecture (or being precise three conjectures): Conjecture For every funcoid $latex f: \prod A\rightarrow\prod B$ (where $latex A$ and $latex B$ are indexed families of sets) there exists a funcoid $latex \Pr^{\left( A \right)}_k f$ defined by the formula $latex […]
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 […]