Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂
T. Banakh ; R. Voytsitskyy
Colloquium Mathematicae, Tome 111 (2008), p. 223-229 / Harvested from The Polish Digital Mathematics Library
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It is shown that the hyperspace CldH(X) (resp. BddH(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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:283683 
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T. Banakh; R. Voytsitskyy. Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂. Colloquium Mathematicae, Tome 111 (2008) pp. 223-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-2-4/