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

Tom 113 / 2008

T. Banakh, R. Voytsitskyy 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
    Akademia Świ/etokrzyska
    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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek