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

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

2008-03-14

arxiv.org/abs/0803.2098v1

Mathematics

Geometric Topology

6 pages. Matem. Studii. 2008 (to appear)

Scientific paper

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.

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