# Wijsman hyperspaces of non-separable metric spaces

Rodrigo Hernández-Gutiérrez; Paul J. Szeptycki

Fundamenta Mathematicae (2015)

- Volume: 228, Issue: 1, page 63-79
- ISSN: 0016-2736

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topRodrigo Hernández-Gutiérrez, and Paul J. Szeptycki. "Wijsman hyperspaces of non-separable metric spaces." Fundamenta Mathematicae 228.1 (2015): 63-79. <http://eudml.org/doc/283021>.

@article{RodrigoHernández2015,

abstract = {Given a metric space ⟨X,ρ⟩, consider its hyperspace of closed sets CL(X) with the Wijsman topology $τ_\{W(ρ)\}$. It is known that $⟨CL(X),τ_\{W(ρ)\}⟩$ is metrizable if and only if X is separable, and it is an open question by Di Maio and Meccariello whether this is equivalent to $⟨CL(X),τ_\{W(ρ)\}⟩$ being normal. We prove that if the weight of X is a regular uncountable cardinal and X is locally separable, then $⟨CL(X),τ_\{W(ρ)\}⟩$ is not normal. We also solve some questions by Cao, Junnila and Moors regarding isolated points in Wijsman hyperspaces.},

author = {Rodrigo Hernández-Gutiérrez, Paul J. Szeptycki},

journal = {Fundamenta Mathematicae},

keywords = {metric space; hyperspace; Wijsman; normal; separable},

language = {eng},

number = {1},

pages = {63-79},

title = {Wijsman hyperspaces of non-separable metric spaces},

url = {http://eudml.org/doc/283021},

volume = {228},

year = {2015},

}

TY - JOUR

AU - Rodrigo Hernández-Gutiérrez

AU - Paul J. Szeptycki

TI - Wijsman hyperspaces of non-separable metric spaces

JO - Fundamenta Mathematicae

PY - 2015

VL - 228

IS - 1

SP - 63

EP - 79

AB - Given a metric space ⟨X,ρ⟩, consider its hyperspace of closed sets CL(X) with the Wijsman topology $τ_{W(ρ)}$. It is known that $⟨CL(X),τ_{W(ρ)}⟩$ is metrizable if and only if X is separable, and it is an open question by Di Maio and Meccariello whether this is equivalent to $⟨CL(X),τ_{W(ρ)}⟩$ being normal. We prove that if the weight of X is a regular uncountable cardinal and X is locally separable, then $⟨CL(X),τ_{W(ρ)}⟩$ is not normal. We also solve some questions by Cao, Junnila and Moors regarding isolated points in Wijsman hyperspaces.

LA - eng

KW - metric space; hyperspace; Wijsman; normal; separable

UR - http://eudml.org/doc/283021

ER -

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