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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)

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

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Hyperspaces homeomorphic to Hilbert space
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by D. W. Curtis PDF
Proc. Amer. Math. Soc. 75 (1979), 126-130 Request permission

Abstract:

The hyperspace ${2^X}$ of a metric space X is the space of nonempty compact subsets, topologized by the Hausdorff metric. It is shown that ${2^X}$ is homeomorphic to the separable Hilbert space ${l^2}$ if and only if X is connected, locally connected, separable, topologically complete, and nowhere locally compact. The principal tool in the proof is Torunczyk’s mapping characterization of ${l^2}$.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 75 (1979), 126-130
  • MSC: Primary 54B20; Secondary 54F65
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0529228-6
  • MathSciNet review: 529228