On compactness and sequential compactness

Levine, Norman

doi:10.1090/S0002-9939-1976-0405357-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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On compactness and sequential compactness
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by Norman Levine PDF

Proc. Amer. Math. Soc. 54 (1976), 401-402 Request permission

Abstract:

Let $X$ be a compact space of cardinality less than or equal to ${\aleph _1}$. It is shown that $X$ is sequentially compact.

References

David Booth, A Bolean view of sequential compactness, Fund. Math. 85 (1974), no. 2, 99–102. MR 367926, DOI 10.4064/fm-85-2-99-102
S. P. Franklin, On two questions of Moore and Mrowka, Proc. Amer. Math. Soc. 21 (1969), 597–599. MR 251696, DOI 10.1090/S0002-9939-1969-0251696-1