On sequence-covering \(msss\) -images of locally separable metric spaces
type: Item
instance of: scholarly article
title: On sequence-covering \(msss\) -images of locally separable metric spaces
zbMATH Open document ID: 1172.54020
DOI: 10.1134/S1995080209010090
author: Nguyen Van Dung
published in: Lobachevskii Journal of Mathematics
publication date: 2009-04-24T00:00:00Z
review text: A function \(f:X\to Y\) is an \(msss\)-mapping if \(X\subset\prod_{n\in\mathbb N}X_n\), a product of metric spaces, and for each \(y\in Y\) there is a sequence \(\langle V_{y,n}\rangle\) of open neighbourhoods of \(y\) so that each \(\pi_n(f^{-1}(V_{y,n}))\) is separable in \(X_n\). Characterisations are given for a space \(X\) to be the \(msss\)-image of a locally separable metric space for various sequence-covering properties of the map involved.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54D55
zbMATH DE Number: 5547324
zbMATH Keywords: msss-mapping
zbMATH Keywords: sequence-covering
zbMATH Keywords: 1-sequence-covering
zbMATH Keywords: 2-sequencecovering
zbMATH Keywords: \(\sigma \)-locally countable
zbMATH Keywords: cs-network
zbMATH Keywords: sn-network
zbMATH Keywords: so-network
MaRDI profile type: Publication
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full work available at URL: s1995080209010090
OpenAlex ID: W2035040943
description: scientific article; zbMATH DE number 5547324