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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On countable compactness and sequential compactness
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by Hao Xuan Zhou PDF
Proc. Amer. Math. Soc. 90 (1984), 121-127 Request permission

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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