A group under \(\text{MA}_{\text{countable}}\) whose square is countably compact but whose cube is not
type: Item
instance of: scholarly article
title: A group under \(\text{MA}_{\text{countable}}\) whose square is countably compact but whose cube is not
zbMATH Open document ID: 0927.54039
DOI: 10.1016/S0166-8641(97)00206-X
author: Artur Hideyuki Tomita
published in: Topology and its Applications
publication date: 1999-12-12T00:00:00Z
review text: The author extends the methods from \textit{K. P. Hart} and \textit{J. van Mill} [Trans. Am. Math. Soc. 323, No. 2, 811-821 (1991; Zbl 0770.54037)] to construct an example as stated in the title as well as, for a given finite~\(k\), a family \(\{H_n:n\in\omega\}\) of topological groups such that a finite product \(\prod_{n\in F} H_n\) is countably compact if{f} \(F\)~has at most \(k\)~elements. As in the aforementioned paper the constructions require \(\text{MA}_{\text{countable}}\) to go through. It is still unknown whether there exist, in ZFC, countably compact groups whose product is not countably compact.
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 03E50
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 1307892
zbMATH Keywords: countably compact
zbMATH Keywords: product
reviewed by: K. P. Hart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1307892