Ultrafilter spaces on the semilattice of partitions

Lorenz Halbeisen; Benedikt Loewe

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arXiv · math/0109176

Ultrafilter spaces on the semilattice of partitions

Lorenz Halbeisen·Benedikt Loewe

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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.

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BibTeX RIS

Lorenz Halbeisen, Benedikt Loewe. 2001-09-23. Ultrafilter spaces on the semilattice of partitions. https://arxiv.org/abs/math/0109176

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