Math Research of Victor Porton

Chain-meet-closed sets on complete lattices

Let is a complete lattice. I will call a filter base a nonempty subset of such that . I will

Conjecture Let and are filters on a set . Then [corrected] This conjecture can be equivalently reformulated in terms of

Let is a set. A filter (on ) is a non-empty set of subsets of such that . Note that

(In a past version of this article I erroneously concluded that our main conjecture follows from join-closedness of .) Let

Let is a set. A filter (on ) is by definition a non-empty set of subsets of such that .

I have proved this conjecture: Theorem 1 If is the set of filter objects on a set then is the

This conjecture has a seemingly trivial case when is a principal filter. When I attempted to prove this seemingly trivial

There were much talking about writing math research articles collaboratively but no real action. I present probably the first real

I conjectured certain formula for the complete lattice generated by a strong partitioning of an element of complete lattice. Now

In this post I defined strong partitioning of an element of a complete lattice. For me it was seeming obvious