abstract
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Ultrafilter spaces on the semilattice of partitions

Lorenz Halbeisen and Benedikt Löwe

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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.