Dense minimal pseudocompact subgroups of compact Abelian groups
type: Item
instance of: scholarly article
title: Dense minimal pseudocompact subgroups of compact Abelian groups
zbMATH Open document ID: 1167.22002
author: Anna Giordano Bruno
published in: Topology and its Applications
publication date: 2008-11-12T00:00:00Z
full work available at URL: http://hdl.handle.net/11390/688723
review text: A Hausdorff topological group \(G\) is pseudocompact if every continuous real-valued function on \(G\) is bounded. Motivated by a noteworthy theorem of \textit{W. W. Comfort} and \textit{J. van Mill} [Proc. Am. Math. Soc. 135, 4039--4044 (2007; Zbl 1138.22002)], which guarantees that a pseudocompact abelian group \(G\) has a proper dense pseudocompact subgroup if and only if \(G\) is non-metrizable, the author studies pseudocompact abelian groups which admit proper dense pseudocompact subgroups satisfying other conditions. In this direction she establishes two results valid in the context of compact abelian groups. First, she obtains necessary and sufficient conditions for such a topological group to admit some proper dense essential pseudocompact subgroup. Second, she obtains necessary and sufficient conditions for such a topological group to admit some proper dense essential subgroup. Some open problems are included in the paper.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 54D25
zbMATH DE Number: 5365204
zbMATH Keywords: pseudocompact groups
zbMATH Keywords: compact abelian groups
zbMATH Keywords: essential groups
zbMATH Keywords: minimal groups
reviewed by: Dinamérico P. Pombo jun.
MaRDI profile type: Publication
OpenAlex ID: W2043587270
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DOI: 10.1016/J.TOPOL.2007.04.020
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description: scientific article; zbMATH DE number 5365204