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 ${l^2}$.References
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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