A weakening of submetrizability and properties of spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1346.54010
publication date: 2016-04-15T00:00:00Z
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 6569372
zbMATH Keywords: weakly jointly compact-metrizable
zbMATH Keywords: jointly compact-metrizable
zbMATH Keywords: wJCM-space
zbMATH Keywords: JCM-space
author: A. V. Arhangel'skii
author: Mitrofan M. Choban
MaRDI profile type: Publication
title: A weakening of submetrizability and properties of spaces
published in: Topology Proceedings
review text: A topological space \(X\) is \textit{weakly jointly compact-metrizable}, briefly a wJCM-space, if there exists a metric \(d\) on \(X\) which metrizes all compact metrizable subspaces of \(X\). Obviously, JCM-spaces (introduced in [\textit{A. V. Arhangel'skii} et al., Topology Appl. 169, 2--15 (2014; Zbl 1294.54005)]), are weakly jointly compact-metrizable. The paper examines this newly introduced concept of wJCM-space. A sample result, see Corollary 3.2, says: Let \(f:X\to Y\) be a perfect mapping of a wJCM-space \(X\) onto a metrizable space \(Y\). If the fibres \(f^{-1}(y)\), where \(y\in Y\), are metrizable, then \(X\) is metrizable.
reviewed by: Szymon Plewik
description: scientific article; zbMATH DE number 6569372