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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Dense subgroups of compact groups


Author: Howard J. Wilcox
Journal: Proc. Amer. Math. Soc. 28 (1971), 578-580
MSC: Primary 22.10
DOI: https://doi.org/10.1090/S0002-9939-1971-0280640-5
MathSciNet review: 0280640
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Abstract: A new short proof is given showing that infinite compact groups contain dense pseudocompact subgroups of small cardinality. Relationships between connectedness and divisibility in pseudocompact groups are given. It is shown that most compact connected Abelian groups contain proper dense connected subgroups.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0280640-5
Keywords: Compact group, dense pseudocompact subgroup, divisible subgroup, dense proper connected subgroup
Article copyright: © Copyright 1971 American Mathematical Society