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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topologically complete groups


Author: Lawrence G. Brown
Journal: Proc. Amer. Math. Soc. 35 (1972), 593-600
MSC: Primary 22A05
MathSciNet review: 0308321
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Abstract: Topologically complete groups are characterized by the existence of a compact subgroup such that the coset space is topologically complete and metrizable. Coset spaces of topologically complete groups and extensions of one topologically complete group by another are again topologically complete. The open mapping theorem is valid for topologically complete groups.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0308321-0
PII: S 0002-9939(1972)0308321-0
Keywords: Topological group, topologically complete, coset space, metrizable uniform space, open mapping
Article copyright: © Copyright 1972 American Mathematical Society