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Proceedings of the American Mathematical Society

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



Semidirect products of topological groups with equal uniformities

Authors: R. W. Bagley and K. K. Lau
Journal: Proc. Amer. Math. Soc. 29 (1971), 179-182
MSC: Primary 22.10
MathSciNet review: 0274645
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Abstract: If $ H \circlebin{s} K$ is a semidirect product such that the automorphisms of $ K$ induced by $ H$ are inner automorphisms, $ H$ has equal uniformities and $ K$ is compact, then $ H \circlebin{s} K$ has equal uniformities. Other closely related results are obtained and used to give an alternate proof that a semidirect product $ V \circlebin{s} K$ of a vector group and a compact group is isomorphic to the direct product $ V \times K$.

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Keywords: Semidirect products of topological groups, equal uniformities, compact groups
Article copyright: © Copyright 1971 American Mathematical Society

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