English

Conglomerated filters, statistical measures, and representations by ultrafilters

Functional Analysis 2020-12-08 v1 General Topology

Abstract

Using a new concept of conglomerated filter we demonstrate in a purely combinatorial way that none of Erd\"{o}s-Ulam filters or summable filters can be generated by a single statistical measure and consequently they cannot be represented as intersections of countable families of ulrafilters. Minimal families of ultrafilters and their intersections are studied and several open questions are discussed.

Keywords

Cite

@article{arxiv.2012.02866,
  title  = {Conglomerated filters, statistical measures, and representations by ultrafilters},
  author = {Vladimir Kadets and Dmytro Seliutin},
  journal= {arXiv preprint arXiv:2012.02866},
  year   = {2020}
}