On pseudocompact and perfectly normal spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1974 English Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Academiae Scientiarum Hungaricae, volume 25, pages 289-290 (issn: 0001-5954, eissn: 1588-2632,

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Authors: Makkouk, A.;

doi: 10.1007/bf01886087

On pseudocompact and perfectly normal spaces

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Abstract

It is shown in this paper that a pseudocompact space is perfectly normal if and only if every closed subset of that space has a countable local base. It follows that, for topological spaces such that each Closed subset has a countable local base, the notions of pseudo-compacity and countable compacity are equivalent.

Related Organizations

Lebanese University
Lebanon
Lebanese German University
Lebanon

Keywords

Compactness, Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

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