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.
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.
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.