Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂

• Autorzy: T. Banakh , R. Voytsitskyy
• Języki publikacji: EN

Abstrakty

EN

It is shown that the hyperspace $Cld_{H}(X)$ (resp. $Bdd_{H}(X)$) 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.

Kategorie tematyczne

• 54B20: Hyperspaces
• 57N20: Topology of infinite-dimensional manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 113
• Numer: 2
• Strony: 223-229

Daty

wydano

2008

Twórcy

autor

T. Banakh

• Instytut Matematyki, Akademia Świętokrzyska, Kielce, Poland
• Department of Mathematics, Ivan Franko Lviv National University, Lviv, Ukraine

autor

R. Voytsitskyy

• Department of Mathematics, Ivan Franko Lviv National University, Lviv, Ukraine

Identyfikatory

DOI

10.4064/cm113-2-4