On the density and products of spaces
type: Item
instance of: scholarly article
title: On the density and products of spaces
zbMATH Open document ID: 1442.54005
published in: Topology and its Applications
publication date: 2020-04-07T00:00:00Z
review text: Extending an earlier result of the author to higher cardinalities it is shown that for a family \(\{X_\alpha \mid \alpha\in 2^\kappa\}\) of spaces each of density \(\kappa\), a cardinal \(>\omega\), the product space \(\prod_{\alpha\in2^\kappa}X_\alpha\) contains a dense subset \(D\) of cardinality \(\kappa\) such that for every \(C\subset D\) of cardinality \(\kappa\) there is \(\alpha\in 2^\kappa\) such that the projection of \(C\) onto \(X_\alpha\) is dense in \(X_\alpha\).
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54B10
zbMATH DE Number: 7187650
zbMATH Keywords: Tychonoff product
zbMATH Keywords: independent matrix
zbMATH Keywords: dense set
author: A. A. Gryzlov
reviewed by: David B. Gauld
MaRDI profile type: Publication
full work available at URL: j.topol.2019.107003
OpenAlex ID: W2995636015
cites work: Q4150804
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cites work: A Sequentially Closed Countable Dense Subset of I 1
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Wikidata QID: Q126590142
DOI: 10.1016/J.TOPOL.2019.107003
description: scientific article; zbMATH DE number 7187650