Compactness and compactifications in generalized topology

摘要

A generalized topology in a set X is a collection Cov(X) of families of subsets of X such that the triple (X, boolean OR Cov(X), Cov(X)) is a generalized topological space (a gts) in the sense of Delfs and Knebusch. In this work, a new notion of a strict compactification of a generalized topological space is introduced and investigated in ZF. The Ultrafilter Theorem (in abbreviation UFT) is shown to be equivalent to the compactness of every Wallman extension of an arbitrary semi-normal space. Th