Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
MathSciNet review: 722428
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Abstract: If a countably compact $ {T_3}$ space $ X$ can be expressed as a union of less then $ c$ many first countable subspaces, then MA implies that $ X$ is sequentially compact. Also MA implies that every countably compact space of size $ < c$ is sequentially compact. However, there is a model of ZFC in which $ {\omega _1} < c$ and there is a countably compact, separable $ {T_2}$ space of size $ {\omega _1}$, which is not sequentially compact.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722428-3
Keywords: Martin's Axiom (MA), iterated forcing
Article copyright: © Copyright 1984 American Mathematical Society