On \(\Sigma\)-products of semi-stratifiable spaces
type: Item
instance of: scholarly article
title: On \(\Sigma\)-products of semi-stratifiable spaces
zbMATH Open document ID: 0607.54005
DOI: 10.1016/0166-8641(87)90071-X
author: Yukinobu Yajima
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The author continues the study of separation properties of \(\Sigma\)- products (i.e. subspaces of infinite Cartesian products of spaces consisting of all points which differ from one fixed point in at most countably many coordinates). Among other results, it is proved that (1) Let \(\Sigma\) be a \(\Sigma\)-product of semi-stratifiable spaces, each finite subproduct of which is paracompact. (a) If \(\Sigma\) has countable tightness then it is normal, (b) If \(\Sigma\) is normal then \(\Sigma\) is collectionwise normal. (2) A \(\Sigma\)-product of semi-stratifiable spaces is subnormal and a P-space.
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54E20
zbMATH DE Number: 3982028
zbMATH Keywords: countable metacompactness
zbMATH Keywords: paracompactness
zbMATH Keywords: collectionwise normality
zbMATH Keywords: separation properties
zbMATH Keywords: \(\Sigma \)-products
zbMATH Keywords: semi-stratifiable spaces
zbMATH Keywords: countable tightness
reviewed by: Carlos R. Borges
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3982028