The weight of a countably compact group whose cardinality has countable cofinality
type: Item
instance of: scholarly article
title: The weight of a countably compact group whose cardinality has countable cofinality
zbMATH Open document ID: 1068.54040
author: Artur Hideyuki Tomita
published in: Topology and its Applications
publication date: 2005-06-01T00:00:00Z
review text: The author obtains a forcing model in which there exists an ultrafilter \(p\) and a \(p\)-compact group whose weight is strictly greater than the cardinality of the group. The cardinality of this group has countable cofinality. As a result, he shows that it is consistent that one can induce on each Boolean group of cardinality \(\lambda \in [c, 2^c]\) a \(p\)-compact group topology of weight strictly larger than \(\lambda\). In the constructed model, CH holds. The work is done in response to the question posed by \textit{E. K. van Douwen} [Proc. Am. Math. Soc. 80, 678--682 (1980; Zbl 0446.54011)], who showed that under GCH any pseudocompact Tychonoff space whose cardinality has countable cofinality, must have cardinality equal to its weight.
reviewed by: S. U. Raczkowski
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 2173264
zbMATH Keywords: forcing
zbMATH Keywords: countably compact group
zbMATH Keywords: \(p\)-group
zbMATH Keywords: weight
MaRDI profile type: Publication
full work available at URL: j.topol.2004.11.016
OpenAlex ID: W2019961465
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DOI: 10.1016/J.TOPOL.2004.11.016
description: scientific article; zbMATH DE number 2173264