There Is a Katĕtov Space That Is Not Countably Paracompact
Keywords:
countably paracompact, Katětov space, Dowker spaceAbstract
We construct, in ZFC, a Katětov space that is not countably paracompact. This answers a question of M. Katětov [Extension of locally finite coverings (Russian), Colloq. Math. 6 (1958), 145-151] and Teodor C. Przymusiński and Michael L. Wage [Collectionwise normality and extensions of locally finite coverings, Fund. Math. 109 (1980), no. 3, 175-187].
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M. Katětov, Extension of locally finite coverings (Russian), Colloq. Math. 6 (1958), 145-151.
Teodor C. Przymusiński and Michael L. Wage, Collectionwise normality and extensions of locally finite coverings, Fund. Math. 109 (1980), no. 3, 175-187.
