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On countably compact topologies on compact groups and on dyadic compacta. (English) Zbl 0804.54001
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.
Reviewer: B.F.Šmarda (Brno)

MSC:
54A05 Topological spaces and generalizations (closure spaces, etc.)
20K45 Topological methods for abelian groups
22C05 Compact groups
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