Wijsman hyperspaces of non-separable metric spaces

• Autorzy: Rodrigo Hernández-Gutiérrez , Paul J. Szeptycki
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54B20: Hyperspaces
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 1
• Strony: 63-79

Daty

wydano

2015

Twórcy

autor

Rodrigo Hernández-Gutiérrez

• Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada

autor

Paul J. Szeptycki

• Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada

Identyfikatory

DOI

10.4064/fm228-1-5