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Proceedings of the American Mathematical Society

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

 

 

Uniform structure in topological groups


Author: Gerald Itzkowitz
Journal: Proc. Amer. Math. Soc. 57 (1976), 363-366
MSC: Primary 22D05
DOI: https://doi.org/10.1090/S0002-9939-1976-0404518-3
MathSciNet review: 0404518
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Abstract: A characterization is given of those locally compact groups having equivalent right and left uniform structures. It is shown that $ \alpha $-compact locally compact groups have equivalent uniformities iff for each right uniformly discrete set $ B$ such that card $ (B) \leq \alpha $ and each neighborhood $ U$ of $ e,{ \cap _{x \in B}}xU{x^{ - 1}}$ is a neighborhood of $ e$. It is also shown that a group is not unimodular iff it contains an open $ \sigma $-compact group which is not unimodular.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0404518-3
Keywords: Equivalent uniform structure, $ \alpha $-compact, unimodular
Article copyright: © Copyright 1976 American Mathematical Society