### A conjecture about multifuncoids and ultrafilters is proved

I’ve proved the following conjecture: Theorem Let $latex f$ be a staroid such that $latex (\mathrm{form}\, f)_i$ is an atomic lattice for each $latex i \in \mathrm{arity}\, f$. We have \$latex \displaystyle L \in \mathrm{GR}\, f \Leftrightarrow \mathrm{GR}\, f \cap \prod_{i \in…

### A filter which cannot be partitioned into ultrafilters

I’ve proved: There exists a filter which cannot be (both weakly and strongly) partitioned into ultrafilters. It is an easy consequence of a lemma proved by Niels Diepeveen (also Karl Kronenfeld has helped me to elaborate the proof). See the preprint of…

### Orderings of filters in terms of reloids – online draft

I put a preliminary draft (not yet checked for errors) of the article “Orderings of filters in terms of reloids” at Algebraic General Topology site. The abstract Orderings of filters which extend Rudin-Keisler preorder of ultrafilters are defined in terms of reloids…

### Isomorphic filters – open problems

For filters on sets defined equivalence relation being isomorphic. Posed some open problems like this: are every two nontrivial ultrafilters isomorphic?