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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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First countable hyperspaces
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by R. E. Smithson PDF
Proc. Amer. Math. Soc. 56 (1976), 325-328 Request permission

Abstract:

An example is given which shows that the space of compact subsets $\mathcal {K}(X)$ of a first countable space $X$ need not be first countable in the finite topology. Further, it is shown that if $\mathcal {K}(X)$ is first countable then each compact subset of $X$ is separable. Finally a characterization of $\mathcal {K}(X)$ first countable in terms of a weak second countability condition is derived.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 325-328
  • MSC: Primary 54B20
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0402667-7
  • MathSciNet review: 0402667