Compatible group topologies
| Autor: | Kevin J. Sharpe |
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| Rok vydání: | 1975 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 53:237-239 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1975-0396830-0 |
| Popis: | 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 A 1 {\mathcal {A}_1} and A 2 {\mathcal {A}_{_2}} . Suppose A 1 {\mathcal {A}_1} is locally compact and A 2 {\mathcal {A}_2} is locally countably compact, and there is a non-void A 2 {\mathcal {A}_2} -open set contained in some A 1 {\mathcal {A}_1} -Lindelöf set. Then A 1 ⊆ A 2 {\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 σ \sigma -compact, and they are compatible. |
| Databáze: | OpenAIRE |
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