Hyperspaces with the Attouch-Wets topology homeomorphic to $l_2$

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Voytsitskyy, Rostyslav
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Abstract
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It is shown that the hyperspace of all nonempty closed subsets $\Cld_{AW}(X)$ of a separable metric space $X$ endowed with the Attouch-Wets topology is homeomorphic to a separable Hilbert space if and only if the completion of $X$ is proper, locally connected and contains no bounded connected component, $X$ is topologically complete and not locally compact at infinity.
Comment: 6 pages. Matem. Studii. 2008 (to appear)
Keywords
Mathematics - Geometric Topology, Mathematics - General Topology, 54B20, 57N20
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