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

• Autores: Ofelia T. Alas, Mikhail G. Tkachenko , Richard G. Wilson
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 149-158
• Idioma: inglés
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• Resumen

  • 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).