Ultrafilter spaces on the semilattice of partitions

Details Ultrafilter spaces on the semilattice of partitions Ultrafilter spaces on the semilattice of partitions

2001-09-23

arxiv.org/abs/math/0109176v1

Topology and its Applications 115(3) (2001) 317-332

Mathematics

Logic

Scientific paper

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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