Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂
Colloquium Mathematicae (2008)
- Volume: 113, Issue: 2, page 223-229
- ISSN: 0010-1354
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topT. Banakh, and R. Voytsitskyy. "Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂." Colloquium Mathematicae 113.2 (2008): 223-229. <http://eudml.org/doc/283683>.
@article{T2008,
abstract = {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.},
author = {T. Banakh, R. Voytsitskyy},
journal = {Colloquium Mathematicae},
keywords = {Hausdorff metric; Hilbert space; hyperspace},
language = {eng},
number = {2},
pages = {223-229},
title = {Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂},
url = {http://eudml.org/doc/283683},
volume = {113},
year = {2008},
}
TY - JOUR
AU - T. Banakh
AU - R. Voytsitskyy
TI - Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂
JO - Colloquium Mathematicae
PY - 2008
VL - 113
IS - 2
SP - 223
EP - 229
AB - 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.
LA - eng
KW - Hausdorff metric; Hilbert space; hyperspace
UR - http://eudml.org/doc/283683
ER -
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