The Character of Certain Closed Sets

Swardson, Mary Anne

Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 38-57

Résumé

Let X be a topological space and let A ⊂ X. The character of A in X is the minimal cardinal of a base for the neighborhoods of A in X. Previous studies have shown that the character of certain subsets of X (or of X2 ) is related to compactness conditions on X. For example, in [12], Ginsburg proved that if the diagonal of a space X has countable character in X2, then X is metrizable and the set of nonisolated points of X is compact. In [2], Aull showed that if every closed subset of X has countable character, then the set of nonisolated points of X is countably compact. In [18], we noted that if every closed subset of X has countable character, then MA + ┐ CH (Martin's axiom with the negation of the continuum hypothesis) implies that X is paracompact.

Détail

DOI : 10.4153/CJM-1984-004-1

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