2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62250The 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.Logic54A05; 54D80; 54A10; 03E17; 03E35text