The Number of Closed Subsets of a Topological Space

Hodel, R. E.

Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 301-314

Résumé

Let X be an infinite topological space, let n be an infinite cardinal number with n ≦ |X|. The basic problem in this paper is to find the number of closed sets in X of cardinality n. A complete answer to this question for the class of metrizable spaces has been given by A. H. Stone in [31], where he proves the following result. Let X be an infinite metrizable space of weight m, let n ≦ |X|.

Détail

DOI : 10.4153/CJM-1978-027-7

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