On product of an arbitrary family of funcoids
I previously defined product of two funcoids. Now the description of product of two funcoids is integrated into my article about multifuncoids. In this article I now also define product of an arbitrary (possibly infinite) family of multifuncoids. The article is yet a very rough preliminary partial draft. The relations of my definition of product […]
Polymath problem: Difference of two filters
My open problem first published in this my blog post (about pair-wise equality of four different expressions for differences of two filters) may be considered to be the next polymath problem. Well, I realize that this may problem may be not ideal for polymath, because to approach a solution of this problem not inventing my […]
A draft about multifuncoids
I put online a rough preliminary draft about multifuncoids, a generalization of funcoids. It contains a few definitions, and theorems. Probably the most interesting thing in it is what I call graph-composition of multifuncoids. The draft contains several open problems.
“Upgrading a Multifuncoid” article upgraded
Now my article Upgrading a Multifuncoid is updated. The main change is that it now contains the conjecture “Upgrading a completary multifuncoid is a completary multifuncoid” (see the article for an exact formulation).
My first article is published
My first math article (titled “Filters on Posets and Generalizations”) was recently published in a peer reviewed, open access journal. Why I published my first research article only in the age of 31? See my short autobiography.
Product of two funcoids and product of two funcoids
I’ve put online an article (PDF, a partial draft) where I define product of two morphisms for certain categories. (Such products are pointfree funcoids.) Particularly it is defined product of two funcoids and product of two reloids. It is a more mature version of a draft I put online previously.
Some new theorems
I added the following theorems to Funcoids and Reloids article. The theorems are simple to prove but are surprising, as do something similar to inverting a binary relation which is generally neither monovalued nor injective. Proposition Let $latex f$, $latex g$, $latex h$ are binary relations. Then $latex g \circ f \not\asymp h \Leftrightarrow g […]
I am changing my research field
I failed to make progress in research of product of funcoids, the next thing I should research in my research plan. I also fail to solve any of my open problems. Thus my research is stalled. I hope other people can solve the problems I formulated. Due this crisis I decide to change my research […]
Micronization – the first attempt to define
This is my first attempt to define micronization. Definition Let $latex f$ is a binary relation between sets $latex A$ and $latex B$. micronization $latex \mu (f)$ of $latex f$ is the complete funcoid defined by the formula (for every $latex x \in A$) $latex \left\langle \mu (f) \right\rangle \left\{ x \right\} = \bigcap \left\{ […]
Product funcoids – a first messy draft
Product funcoids [outdated link remove] (not a math article but a messy collection of unproved and not exactly formulated statements). This is my first attempt to define product funcoids. There is needed yet much work to rewrite it as a rigorous math text.