Domination in products
type: Item
instance of: scholarly article
title: Domination in products
zbMATH Open document ID: 1328.54004
author: David Guerrero Sánchez
published in: Topology and its Applications
publication date: 2015-08-19T00:00:00Z
review text: All spaces are Tychonoff. For a space \(X\) denote by \(\mathcal K(X)\) the set of all compact subsets of \(X\). A family \(\mathcal A\) of subsets of \(X\) is fundamental if for every \(K\in\mathcal K(X)\) there is \(A\in \mathcal A\) with \(K\subset A\); \(\mathcal A\) is \(M\)-ordered for some space \(M\) if \(\mathcal A=\{A_K:K\in \mathcal K(M)\}\) and \(K\subset L\) implies \(A_K\subset A_L\). A space \(X\) is \(M\)-dominated (strongly \(M\)-dominated) if it has an \(M\)-ordered (\(M\)-ordered fundamental) compact cover. \textit{D. Guerrero Sánchez} [Topology Appl. 160, No. 13, 1652--1658 (2013; Zbl 1286.54005)] defined the following two cardinal invariants for a space \(X\): the metric domination index of \(X\), \(dm(X) = \min\{w(M) : X \text{ is }M\)-dominated by a metric space \(M\)
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 6473611
zbMATH Keywords: metric domination index
zbMATH Keywords: strong metric domination index
zbMATH Keywords: Lindelöf \(\Sigma\)-space
zbMATH Keywords: function space
zbMATH Keywords: monolithic space
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2015.05.077
OpenAlex ID: W896618331
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DOI: 10.1016/J.TOPOL.2015.05.077
description: scientific article; zbMATH DE number 6473611