On the widest class of completeness-preserving covering maps
type: Item
instance of: scholarly article
title: On the widest class of completeness-preserving covering maps
zbMATH Open document ID: 1485.54035
published in: Topology and its Applications
publication date: 2022-02-09T00:00:00Z
review text: The author [Topology Appl. 201, 269--273 (2016; Zbl 1337.54020)] sought for the widest class \(\mathfrak{H}\) of maps \(f: X\to Y\) between separable metrizable spaces that satisfies the following conditions: (1)\, Maps \(f\) from \(\mathfrak{H}\) are determined by their behaviour on some countable compact sets from \(Y\); (2)\, If \(X\) is a Polish space, then \(Y\) is also a Polish space; (3)\, Suppose \(f: X\to Y\) and \(g: Y\to Z\) are maps. If \(f\) and \(g\) belong to \(\mathfrak{H}\), then so does \(g\circ f\). In this paper \(H\)-covering maps are introduced and it is proposed that the class of \(H\)-covering continuous maps is the class \(\mathfrak{H}\). Finally, the author analyzes the following three kinds of maps in separable metric spaces: \(H\)-covering maps, \(s\)-covering maps and tri-quotient maps.
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 03D99
zbMATH DE Number: 7471574
zbMATH Keywords: Polish space
zbMATH Keywords: \(s\)-covering map
zbMATH Keywords: compact-covering map
zbMATH Keywords: tri-quotient map
zbMATH Keywords: transquotient map
zbMATH Keywords: stable map
zbMATH Keywords: \(H\)-covering map
author: Alexey Ostrovsky
reviewed by: Shou Lin
MaRDI profile type: Publication
full work available at URL: j.topol.2021.107998
OpenAlex ID: W4206441016
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DOI: 10.1016/J.TOPOL.2021.107998
description: scientific article; zbMATH DE number 7471574