Shrinking property in \(\Sigma\)-products of paracompact p-spaces
type: Item
instance of: scholarly article
title: Shrinking property in \(\Sigma\)-products of paracompact p-spaces
zbMATH Open document ID: 0576.54030
DOI: 10.1016/0166-8641(85)90063-X
author: Attilio Le Donne
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: This paper is devoted to the study of the shrinking property of a \(\Sigma\)-product of spaces; a space is said to have the shrinking property if for every open cover \(\{U_{\lambda}| \lambda \in \Lambda \}\) there exists an open cover \(\{V_{\lambda}| \lambda \in \Lambda \}\) with \(\bar V_{\lambda}\subset U_{\lambda}\) for each \(\lambda\in \Lambda\). The main result is that a \(\Sigma\)-product of paracompact p-spaces with countable tightness has the shrinking property. As a corollary, by using a theorem of \textit{A. P. Kombarov} [Sov. Math., Dokl. 19, 403-407; Dokl. Akad. Nauk SSSR 239, 775-778 (1978; Zbl 0397.54013)] it is also mentioned that a \(\Sigma\)-product of paracompact p-spaces has the shrinking property iff it is normal.
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54E18
Mathematics Subject Classification ID: 54B10
zbMATH DE Number: 3921496
zbMATH Keywords: shrinking property
zbMATH Keywords: \(\Sigma \) -product
zbMATH Keywords: paracompact p-spaces with countable tightness
MaRDI profile type: Publication
cites work: Q5327711
cites work: Normality in Subsets of Product Spaces
cites work: Q4180930
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cites work: Q4054355
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cites work: The Shrinking Property
full work available at URL: 0166-8641(85)90063-x
OpenAlex ID: W2079811927
description: scientific article; zbMATH DE number 3921496