Ultrafilter spaces on the semilattice of partitions
Logic
2007-05-23 v1
Abstract
The Stone-Cech compactification of the natural numbers bN, or equivalently, the space of ultrafilters on the subsets of omega, is a well-studied space with interesting properties. If one replaces the subsets of omega by partitions of omega, one can define corresponding, non-homeomorphic spaces of partition ultrafilters. It will be shown that these spaces still have some of the nice properties of bN, even though none is homeomorphic to bN. Further, in a particular space, the minimal height of a tree pi-base and P-points are investigated.
Keywords
Cite
@article{arxiv.math/0109176,
title = {Ultrafilter spaces on the semilattice of partitions},
author = {Lorenz Halbeisen and Benedikt Loewe},
journal= {arXiv preprint arXiv:math/0109176},
year = {2007}
}