I am not doing math research this month (because a bug in TeXmacs software which I use for writing my book and articles). I instead do writing some free software not to waste my time. But today (this hour) I unexpectedly had…
read moreWhen my book was already sent to a publisher, I decided to rewrite it. Here is my rewriting plan (what I am going to change in the book).
read moreIn this short note I describe four sets (including the set of filters itself) which bijectively correspond to the set of filters on a poset. I raise the question: How to denote all these four posets and their principal elements? Please write…
read moreI have corrected some errors in my book related to my definition of multifuncoids. The definition of multifuncoid was wrong and this triggered several errors along my book.
read moreAfter checking for errors I added (as a new chapter) materials of the article Identity staroids into my research monograph. I plan to “dissolve” this chapter, that is distribute its materials among other chapters and liquidate this chapter itself.
read moreI’ve mostly finished writing the article Identity Staroids which considers $latex n$-ary identity staroids (with possibly infinite $latex n$), which generalize $latex n$-ary identity relations and some related topics. (In my theory there are two kinds of identity staroids: big and small…
read moreI have uploaded a new version of my book with an error corrected: the definition of principal staroids and some related stuff were wrong.
read moreConjecture: Every time when an unproved result seems obvious, we refer to an unproved conjecture (from which it follows) in our mind
read moreToday I have noticed a new simple to prove theorem which is missing in my article: Theorem If $latex ( \mathfrak{A}; \mathfrak{Z})$ is a join-closed filtrator and both $latex \mathfrak{A}$ and $latex \mathfrak{Z}$ are complete lattices, then for every $latex S \in…
read moreOpen problem Let $latex A$ and $latex B$ be infinite sets. Characterize the set of all coatoms of the lattice $latex \mathsf{FCD}(A;B)$ of funcoids from $latex A$ to $latex B$. Particularly, is this set empty? Is $latex \mathsf{FCD}(A;B)$ a coatomic lattice? coatomistic…
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