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

Continue reading# Month: October 2009

## Principal filters are center – solved

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

Continue reading## Are principal filters the center of the lattice of filters?

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

Continue reading## Collaborative math research – a real example

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

Continue reading## Complete lattice generated by a partitioning – finite meets

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

Continue reading## Complete lattice generated by a partitioning of a lattice element

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

Continue reading## Partitioning elements of distributive and finite lattices

I proposed this open problem for the next polymath project. Now I will consider some its special simple cases.

Continue reading## Proposal: Partitioning a lattice element

I’ve given two different definitions for partitioning an element of a complete lattice (generalizing partitioning of a set). I called

Continue reading## Partitioning of a lattice element: a conjecture

Let is a complete lattice. Let . I will call weak partitioning of a set such that . I will

Continue reading