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.

read moreI’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…

read moreI 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…

read moreI 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…

read moreThis 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…

read moreProduct funcoids [outdated link remove] (not a math article but a messy collection of unproved and not exactly formulated statements).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…

read moreI updated the article Orderings of filters in terms of reloids from “preliminary draft” to just “draft”. It means most errors are corrected and now you can read it.

read moreI solved the first problem from this blog post (see Funcoids and Reloids article for a solution). It opens the path for solving several other open problems which seem to be its consequences.

read moreI will outline which open problems follow from other open problems. In this post I don’t enter into gory details how to prove these implications, because these are useless without a prior proof of the main premise. I write these notes just…

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