Uniform structure in topological groups
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- by Gerald Itzkowitz PDF
- Proc. Amer. Math. Soc. 57 (1976), 363-366 Request permission
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.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- 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