Quasi-metrizability
type: Item
instance of: scholarly article
title: Quasi-metrizability
zbMATH Open document ID: 0933.54025
DOI: 10.1016/S0166-8641(97)00036-9
author: H. H. Hung
published in: Topology and its Applications
publication date: 2000-03-26T00:00:00Z
review text: The author shows that quasi-(pseudo)metrizability of a topological space \(X\) is equivalent to the availability on \(X\) of a decreasing neighborhood base \((g(n,x))_{n\in \omega}\) at every \(x\in X\) such that for every countable and relatively locally finite \(A\subseteq X\) and \(n\in \omega\) we have \(g(\nu,g(\nu,A))\subseteq g(n,A)\) for some \(\nu\in \omega\) (dependent on \(A\) and \(n\)). The result is inspired by older metrization results of the author and known characterizations of \(\gamma\)-spaces. The proof is based on a result due to \textit{R. Fox} and the reviewer [Arch. Math. 41, 57-63 (1983; Zbl 0504.54028)].
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 54D70
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E55
zbMATH DE Number: 1308051
zbMATH Keywords: \(\gamma\)-space
zbMATH Keywords: cushioned
zbMATH Keywords: local quasi-uniformity
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
cites work: C-complete quasi-uniform spaces
cites work: A Regular Counterexample to the γ-Space Conjecture
cites work: PARACOMPACTNESS AND SUBPARACOMPACTNESS IN PERFECTLY NORMAL LOCALLY COMPACT SPACES
cites work: Spaces defined by sequences of open covers which guarantee that certain sequences have cluster points
cites work: Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity
cites work: Some Metrization Theorems
cites work: A Contribution to the Theory of Metrization
cites work: Q4373423
cites work: Which topologies are quasimetrizable?
cites work: The topology of digital images
cites work: On strongly quasi-metrizable spaces
cites work: Q4326507
cites work: Q3490613
cites work: Q4004593
cites work: Locally Uniform Spaces
cites work: On Quasi-Metric Spaces
full work available at URL: s0166-8641(97)00036-9
OpenAlex ID: W4210254754
description: scientific article; zbMATH DE number 1308051