Resumen de Which topologies have immediate predecessors in the poset of Hausdorff topologies?

Ofelia T. Alas, Mikhail G. Tkachenko , Richard G. Wilson

• It is known that each topology on a set X which is not H-closed has an immediate predecessor in the poset of Hausdorff topologies on X. In this paper, we show that all submaximal H-closed topologies which are not minimal Hausdorff, as well as certain classes of dispersed H-closed topologies, also have such predecessors. We give examples of second countable H-closed topologies which are not upper in this poset, answering in the negative a question of N. Carlson (2007).