My further study plans
I remind that I am not a professional mathematician. Nevertheless I have written research monograph “Algebraic General Topology. Volume 1”. Yesterday I have asked on MathOverflow how to characterize a poset of all filters on a set. From the answer: the posets isomorphic to lattices of filters on a set are precisely the atomic compact […]
A (possibly open) problem about filters on a set
http://mathoverflow.net/questions/139608/a-characterization-of-the-poset-of-filters-on-a-set For the lattices of all subsets of a given set it is known an axiomatic characterization: A poset is isomorphic to a set of all subsets of some set iff it is a complete atomic boolean algebra. The question: How to characterize the sets of filters on a set? That is having a poset, […]
(Not math) My spiritual experience related with the theory of funcoids
This post is not about mathematics. It is about spirituality. In the very beginning of my research, when I was formulating the definition of funcoids I felt certain spiritual experience. While thinking about it, I felt myself in a kind of virtual reality, at the same time not only sitting in a chair but also […]
A new math problem about funcoids
Just a few seconds ago I realized that I have never considered and and even never formulated the following problem: Explicitly describe the set of complemented funcoids. Note that not all principal funcoids are complemented. For example see my book for a proof that the identity funcoid on some set is not complemented.
My conjecture partially solved
I’ve partially solved my conjecture, proposed Polymath problem described at this page. The problem asks which of certain four expressions about filters on a set are always pairwise equal. I have proved that the first three of them are equal, equality with the fourth remains an open problem. For the (partial) solution see this online […]
Partial order funcoids and reloids
Partial order funcoids and reloids formalize such things as “infinitely small” step rotating a circle counter-clockwise. This is “locally” a partial order as every two nearby “small” sets (where we can define “small” for example as having the diameter (measuring along the circle) less than $latex \pi$) are ordered: which is before in the order […]
The history of discovery of funcoids
In my book I introduce funcoids as a generalization of proximity spaces. This is the most natural way to introduce funcoids, but it was not the actual way I’ve discovered them. The first thing discovered equivalent to funcoids was a function $latex \Delta$ (generalizing a topological space) which I defined to get a set as […]
Algebraic General Topology presentation – new version
The PDF Slides about Algebraic General Topology were updated to match newer notation used in my book. Use these slides to quickly familiarize yourself with my theory. I’ve removed altogether the notion of filter object, instead using a new different notation of lattice operators.
A mathematical theory of singularities!
I present my mathematical theory of singularities. It may probably have applications in general relativity and other physics. The definitions are presented in this short draft article. Before reading this article I recommend to skim through my research monograph (in the field of general topology), because the above mentioned article uses concepts defined in my […]
Two theorems about totally bounded images of a totally bounded reloid
I’ve added to my book two following theorems (formerly conjectures). Theorem Let $latex \mu$ and $latex \nu$ are endoreloids. Let $latex f$ is a principal $latex \mathrm{C}’ ( \mu; \nu)$ continuous, monovalued, surjective reloid. Then if $latex \mu$ is $latex \beta$-totally bounded then $latex \nu$ is also $latex \beta$-totally bounded. Theorem Let $latex \mu$ and […]