Geodesic
Characterizing metric spaces whose hyperspaces are homeomorphic to $\ell _2$
T. Banakh 1   ; R. Voytsitskyy 2
1 Instytut Matematyki Akademia Świ/etokrzyska Kielce, Poland and Department of Mathematics Ivan Franko Lviv National University Lviv, Ukraine
2 Department of Mathematics Ivan Franko Lviv National University Lviv, Ukraine
Colloquium Mathematicum, Tome 113 (2008) no. 2, pp. 223-229 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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It is shown that the hyperspace ${\rm Cld}_{\rm H}(X)$ (resp. ${\rm Bdd}_{\rm H}(X)$) of non-empty closed (resp. closed and bounded) subsets of a metric space $(X,d)$ is homeomorphic to $\ell_2$ if and only if the completion $\overline X$ 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.
DOI : 10.4064/cm113-2-4
Keywords: shown hyperspace cld resp bdd non empty closed resp closed bounded subsets metric space homeomorphic ell only completion overline connected locally connected topologically complete nowhere locally compact each subset resp each bounded subset totally bounded

T. Banakh  1   ; R. Voytsitskyy  2

1 Instytut Matematyki Akademia Świ/etokrzyska Kielce, Poland and Department of Mathematics Ivan Franko Lviv National University Lviv, Ukraine
2 Department of Mathematics Ivan Franko Lviv National University Lviv, Ukraine 
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T. Banakh; R. Voytsitskyy. Characterizing metric
spaces whose hyperspaces are homeomorphic to  $\ell _2$. Colloquium Mathematicum, Tome 113 (2008) no. 2, pp. 223-229. doi: 10.4064/cm113-2-4

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