Abelian torsion groups with a countably compact group topology
type: Item
instance of: scholarly article
title: Abelian torsion groups with a countably compact group topology
zbMATH Open document ID: 1184.54034
published in: Topology and its Applications
publication date: 2009-12-03T00:00:00Z
review text: The main result of the paper is: An Abelian torsion group admits a pseudocompact group topology if and only if it admits a countably compact group topology provided that {\parindent8mm \begin{itemize}\item[(i)] \(\alpha^{\omega}=\alpha\) for every cardinal \(\alpha\) of uncountable cofinality; \item[(ii)] every cardinal of countable cofinality is strong limit; \item[(iii)] there exists a selective ultrafilter on \(\omega\). \end{itemize}}
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 5641743
zbMATH Keywords: torsion group
zbMATH Keywords: countably compact groups
zbMATH Keywords: Ulm-Kaplansky invariants
zbMATH Keywords: selective ultrafilters
author: Irene Castro Pereira
author: Artur Hideyuki Tomita
reviewed by: Igor V. Protasov
MaRDI profile type: Publication
full work available at URL: j.topol.2009.04.051
OpenAlex ID: W2045104250
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DOI: 10.1016/J.TOPOL.2009.04.051
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description: scientific article; zbMATH DE number 5641743