On countably compact topologies on compact groups and on dyadic compacta
type: Item
instance of: scholarly article
title: On countably compact topologies on compact groups and on dyadic compacta
zbMATH Open document ID: 0804.54001
DOI: 10.1016/0166-8641(94)90048-5
published in: Topology and its Applications
publication date: 1994-08-22T00:00:00Z
review text: The author applies certain classical results of S. Mazur, J. Keisler, A. Tarski and N. Th. Varopoulos to the theory of countably compact topological groups. Some results: If \(f\) is a one-to-one continuous mapping of a countably compact topological group of countable tightness onto a compact Hausdorff space \(X\), then \(X\) is metrizable. If a countably compact topological group of countable tightness acts continuously and transitively on a compact Hausdorff space \(X\), then \(X\) is metrizable. The paper contains also many unsolved problems.
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 20K45
Mathematics Subject Classification ID: 22C05
zbMATH DE Number: 600036
zbMATH Keywords: totally bounded groups
zbMATH Keywords: sequentially continuous mappings
zbMATH Keywords: countably compact topological group
author: A. V. Arhangel'skii
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90048-5
OpenAlex ID: W2154083436
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description: scientific article; zbMATH DE number 600036