The number of \(K\)-determination of topological spaces
type: Item
instance of: scholarly article
title: The number of \(K\)-determination of topological spaces
zbMATH Open document ID: 1263.54006
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2013-01-30T00:00:00Z
review text: The paper is a study of two cardinal invariants: the number of \(K\)-determination \(\ell\Sigma\) and the number of Nagami \(Nag\) which are extensions of Lindelöf \(\Sigma\)-spaces and Nagami's spaces to higher cardinals. For a space \(Y\), \(\ell\Sigma(Y)\) (\(Nag(Y)\)) is the smallest infinite cardinal number \(\mathfrak{m}\) for which there are a metric space \(X\) (a space \(X\)) of weight \(\mathfrak{m}\) and an upper semicontinuous compact-valued mapping \(\phi:X \to Y\) such that \(Y = \bigcup\{\phi(x):x\in X\}\). The behaviour of these functions under several topological constructions is investigated, as well as their relationships with other cardinal invariants. For a topological space \(Y\) we have \(\ell(Y) \leq Nag(Y) \leq \ell\Sigma(Y) \leq |Y|\). If \(Y\) is a completely regular space, then \(Nag(Y) = \max\{\Sigma(Y),\ell(Y)\}\), where \(\Sigma(Y)\) is the \(\Sigma\)-degree of \(Y\). There is a space \(Y \subset \beta\mathbb N\) such that \(Nag(Y) \leq w(Y) < \ell\Sigma(Y)\). If \(Y\) is a compact space, then \(\ell\Sigma(C_p(Y)) \leq w(C_p(Y))\).
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 6132871
zbMATH Keywords: cardinal functions
zbMATH Keywords: number of Nagami
zbMATH Keywords: \(\Sigma\)-degree
zbMATH Keywords: Lindelöf \(\Sigma\)-spaces
zbMATH Keywords: \(G_{\delta}\)-diagonal
zbMATH Keywords: usco maps
author: B. Cascales
author: María Muñoz Guillermo
author: José Orihuela
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: s13398-012-0058-6
OpenAlex ID: W2061759251
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DOI: 10.1007/S13398-012-0058-6
description: scientific article; zbMATH DE number 6132871