On countable compactness and sequential compactness

Author:
Hao Xuan Zhou

Journal:
Proc. Amer. Math. Soc. **90** (1984), 121-127

MSC:
Primary 54D30; Secondary 03E35, 03E50, 54A35

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722428-3

MathSciNet review:
722428

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Abstract: If a countably compact space can be expressed as a union of less then many first countable subspaces, then MA implies that is sequentially compact. Also MA implies that every countably compact space of size is sequentially compact. However, there is a model of ZFC in which and there is a countably compact, separable space of size , which is not sequentially compact.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722428-3

Keywords:
Martin's Axiom (MA),
iterated forcing

Article copyright:
© Copyright 1984
American Mathematical Society