Elsevier

Discrete Mathematics

Volume 108, Issues 1–3, 28 October 1992, Pages 31-35
Discrete Mathematics

On the cardinality of certain Hausdorff spaces

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Abstract

We prove (in ZFC) the following theorem. Assume κ is an infinite cardinal, X is a Hausdorff space such that every subspace Y of X is the union of κ compact subsets of Y. Then X has cardinality at most κ.

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Research supported by Hungarian National Foundation, Scientific Research Grant No. 1805.