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Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂

T. BanakhR. Voytsitskyy — 2008

Colloquium Mathematicae

It is shown that the hyperspace C l d H ( X ) (resp. B d d H ( X ) ) of non-empty closed (resp. closed and bounded) subsets of a metric space (X,d) is homeomorphic to ℓ₂ if and only if the completion X̅ of X is connected and locally connected, X is topologically complete and nowhere locally compact, and each subset (resp. each bounded subset) of X is totally bounded.

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