On perfectly normal dense subspaces of products
type: Item
instance of: scholarly article
title: On perfectly normal dense subspaces of products
zbMATH Open document ID: 1111.54022
author: D. P. Baturov
published in: Topology and its Applications
publication date: 2007-02-09T00:00:00Z
review text: It is shown that whenever \(X\) is a separable metric space with more than one point, then \(X^{2^c}\) has a perfectly normal dense subspace which is not collectionwise Hausdorff. This is an interesting answer to a question of \textit{A. V. Arkhangel'skij}, who has asked in [Topological function spaces. Transl. from the Russian by R. A. M. Hoksbergen. Mathematics and its Applications, Soviet Series. 78. Dordrecht etc.: Kluwer Academic Publishers. ix, 205 p. (1992; Zbl 0758.46026)] whether every normal dense subspace of a product of separable metric spaces is collectionwise normal.
reviewed by: Harald Brandenburg
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 5123621
zbMATH Keywords: perfectly normal
zbMATH Keywords: collectionwise normal
zbMATH Keywords: collectionwise Hausdorff
MaRDI profile type: Publication
full work available at URL: j.topol.2006.02.006
OpenAlex ID: W2002679491
cites work: Q3736526
cites work: Normality in dense subspaces of products
cites work: Metrization of Topological Spaces
cites work: Normality in Subsets of Product Spaces
cites work: Q4150804
cites work: On the Notion of n-Cardinality
cites work: Q3345418
DOI: 10.1016/J.TOPOL.2006.02.006
description: scientific article; zbMATH DE number 5123621