A pseudocompact group which is not strongly pseudocompact
type: Item
instance of: scholarly article
title: A pseudocompact group which is not strongly pseudocompact
zbMATH Open document ID: 1330.54045
author: Artur Hideyuki Tomita
author: Salvador Garcia-Ferreira
published in: Topology and its Applications
publication date: 2015-08-19T00:00:00Z
review text: A topological space \(X\) is \textit{strongly pseudocompact} if for every sequence \((U_n)_{n\in\mathbb N}\) of pairwise disjoint non-empty open subsets of \(X\) there exists a sequence \((x_n)_{n\in\mathbb N}\) in \(X\) such that \(x_n\in U_n\) for every \(n\in\mathbb N\) and \(cl_X(\{x_n : n \in\mathbb N\})\setminus\left( \bigcup_{n\in\mathbb N}U_n\right)\neq\emptyset\). It is known that for a topological space \[ \text{countably compact } \Rightarrow \text{ strongly pseudocompact } \Rightarrow \text{ pseudocompact}. \] Examples are known of a pseudocompact space that is not strongly pseudocompact and of a strongly pseudocompact group that is not countably compact. Moreover, for a topological group it is equivalent to be strongly pseudocompact and ultrapseudocompact. In this paper, the authors construct a pseudocompact group that is not strongly pseudocompact.
reviewed by: Anna Giordano Bruno
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 6473610
zbMATH Keywords: topological group
zbMATH Keywords: pseudocompact
zbMATH Keywords: strongly pseudocompact
zbMATH Keywords: ultrapseudocompact
zbMATH Keywords: countably compact
MaRDI profile type: Publication
full work available at URL: j.topol.2015.05.076
OpenAlex ID: W574164152
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DOI: 10.1016/J.TOPOL.2015.05.076
description: scientific article; zbMATH DE number 6473610