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## Characterizing metric spaces whose hyperspaces are homeomorphic to $\ell _2$

### Tom 113 / 2008

Colloquium Mathematicum 113 (2008), 223-229 MSC: 54B20, 57N20. DOI: 10.4064/cm113-2-4

#### Streszczenie

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.

#### Autorzy

• T. BanakhInstytut Matematyki
Kielce, Poland
and
Department of Mathematics
Ivan Franko Lviv National University
Lviv, Ukraine
e-mail
• R. VoytsitskyyDepartment of Mathematics
Ivan Franko Lviv National University
Lviv, Ukraine
e-mail

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