Wijsman and hit-and-miss topologies of quasi-metric spaces
type: Item
instance of: scholarly article
title: Wijsman and hit-and-miss topologies of quasi-metric spaces
zbMATH Open document ID: 1030.54014
author: Jesús Rodríguez-López
author: Salvador Romaguera
published in: Set-Valued Analysis
publication date: 2003-10-14T00:00:00Z
review text: The authors study the relationship between the Wijsman topology and (proximal) hit-and-miss topologies on hyperspaces of quasi-metric spaces. They establish the equivalence of these hypertopologies in terms of Urysohn families of sets. They also show that for quasi-metric spaces \((X,d)\), the Hausdorff extended quasi-pseudo-metric is compatible with the Wijsman hypertopology if and only if \(d^{-1}\) is hereditarily precompact.
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54E30
zbMATH DE Number: 1992539
zbMATH Keywords: (Hausdorff) quasi-pseudo-metric
zbMATH Keywords: (proximal) hit-and-miss topologies
zbMATH Keywords: Wijsman topology
zbMATH Keywords: Vietoris topology
zbMATH Keywords: uniformly Urysohn family
zbMATH Keywords: far Urysohn family
reviewed by: Aleksandr A. Ivanov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1992539