Star-countable \(k\)-networks, and quotient images of locally separable metric spaces
type: Item
instance of: scholarly article
title: Star-countable \(k\)-networks, and quotient images of locally separable metric spaces
zbMATH Open document ID: 0896.54019
DOI: 10.1016/S0166-8641(97)00060-6
published in: Topology and its Applications
publication date: 1998-05-10T00:00:00Z
review text: This paper involves spaces that have star-countable \(k\)-networks, and establishes three kinds of theorems for such spaces. First, a reflection theorem is given showing that such spaces are \(\aleph_{0}\)-spaces whenever every small (cardinality \(\leq\omega_{1}\)) subspace is a separable \(\sigma\)-space. Also \(k\)-spaces having star-countable \(k\)-networks are shown to be quotient (compact-covering) \(s\)-images of locally separable metric spaces if and only if they contain no closed copy of \(S_{\omega_{1}}\). The final result is that the hyperspace of compact subsets of a space \(X\) has a star-countable \(k\)-network if and only if \(X\) does.
Mathematics Subject Classification ID: 54E99
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 1121468
zbMATH Keywords: star-countable cover
zbMATH Keywords: \(k\)-network
zbMATH Keywords: \(k\)-space
zbMATH Keywords: quotient map
zbMATH Keywords: \(s\)-map
zbMATH Keywords: compact map
author: Chuan Liu
author: Y. Tanaka
reviewed by: R. A. McCoy
MaRDI profile type: Publication
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full work available at URL: s0166-8641(97)00060-6
OpenAlex ID: W2043373382
description: scientific article; zbMATH DE number 1121468