WHICH TOPOLOGIES HAVE IMMEDIATE PREDECESSORS IN THE POSET OF HAUSDORFF TOPOLOGIES?

Abstract

We study which topology have an immediate predecessor in the poset of Sigma(2) of Hausdorff topologies on set X. We show that certain classes of H-closed topologies, do have predecessors. and we give examples of second countable H-closed topologies which are not upper Sigma(2.)