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 a new interesting idea about my math research:

Let denote the set of finite joins of funcoidal products of two principal filters.

**Conjecture** The poset of funcoids is order-isomorphic to the set of filters on the set (moreover the isomorphism is (possibly infinite) meet of the filter).

If proved positively, this may reveal new properties of funcoids and probably solve some of my open problems.

When 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).

In 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 to my email any ideas about this.

I 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.

After 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.

I’ve mostly finished writing the article Identity Staroids which considers -ary identity staroids (with possibly infinite ), which generalize -ary identity relations and some related topics. (In my theory there are two kinds of identity staroids: *big* and *small* identity staroids.)

Writing of the article is mostly finished, I am going just to check it for errors and reorder the material.

After finishing with this article, I am going to integrate the article into my research monograph and publish it.

Note that there are several conjectures in my article.

I have uploaded a new version of my book with an error corrected: the definition of principal staroids and some related stuff were wrong.

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