abstract
Ultrafilter spaces on the semilattice of partitions
Lorenz Halbeisen and Benedikt Löwe
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.