Locally contractible coset spaces
| Autor: | Tadeusz Dobrowolski, Sergey Antonyan |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Forum Mathematicum. 27:2157-2175 |
| ISSN: | 1435-5337 0933-7741 |
| DOI: | 10.1515/forum-2013-0033 |
| Popis: | We prove that for any closed subgroup H of a locally compact Hausdorff group G the following properties are mutually equivalent: (1) the coset space G/H is locally contractible, (2) G/H is finite-dimensional and locally connected, (3) G/H is a manifold. Assume that G is a locally compact group with compact space of connected components. If the natural action of G on a locally contractible coset space G/H is effective, then we prove that G is a Lie group. |
| Databáze: | OpenAIRE |
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