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Proceedings of the American Mathematical Society

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Compatible group topologies

Author: Kevin J. Sharpe
Journal: Proc. Amer. Math. Soc. 53 (1975), 237-239
MSC: Primary 22A05
MathSciNet review: 0396830
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Abstract: Two topologies defined on some space are compatible if they contain in common a Hausdorff topology. The following result is proved for two compatible group topologies $ {\mathcal{A}_1}$ and $ {\mathcal{A}_{_2}}$. Suppose $ {\mathcal{A}_1}$ is locally compact and $ {\mathcal{A}_2}$ is locally countably compact, and there is a non-void $ {\mathcal{A}_2}$-open set contained in some $ {\mathcal{A}_1}$-Lindelöf set. Then $ {\mathcal{A}_1} \subseteq {\mathcal{A}_2}$. This result is a stronger version of a theorem by Kasuga, in which two group topologies are shown to be equal if both of them are locally compact and $ \sigma $-compact, and they are compatible.

References [Enhancements On Off] (What's this?)

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Keywords: Compatible group topologies, comparable group topologies, $ \sigma $-compact topological groups
Article copyright: © Copyright 1975 American Mathematical Society

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