Toward formalization of partial infima and suprema

I’ve written a short note about suprema and infima in formal math: Toward formalization of partial infima and suprema It is especially useful for these who do math formally (in proof assistants), but may be inspiring for regular mathematicians too.

Complete relativity theory

Disclaimer: I am not a physicist. Einstein has discovered that some physical properties are relative. In this blog post I present the conjecture that essentially all physical properties are relative. I do not formulate exact details of this theory, a thing which could be measurable, but just a broad class of specific theories. Nevertheless the […]

My math book sent to a competition

I have sent my book “Algebraic General Topology. Volume 1” to EMS Monograph Award competition, which provides a 10000 EUR prize for best math research monograph. I hope to win the prize and also to publish my book with EMS. While the copyright is not yet transferred to a publisher, you may read my draft […]

“Algebraic General Topology. Volume 1” first complete draft

Today I release the first complete (not partial) draft of my book “Algebraic General Topology. Volume 1”. This draft is very rough yet however and needs much editing both for error checking and for greater clarity. It is also possible that I will expand it a little, especially in the chapter “Multifuncoids and staroids”. Download […]

“Algebraic General Topology. Volume 1” – now entire my theory here

The current draft (PDF) of the book “Algebraic General Topology. Volume 1” contains the entire general topology theory which I’ve discovered (so called Algebraic General Topology). Now is a happy day when my entire theory is put into one PDF file (190 A4 pages). In this version of the book are however missing an introductory […]

Funcoids and reloids in my math book draft

My partial draft book now contains the theory of funcoids and reloids. You may use this online draft (while I have not yet transferred the copyright) to study my theory of funcoids and reloids. Pointfree funcoids, multidimensional funcoids and staroids presented in my articles are not yet added to this partial draft.

“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 […]