Topological groups with dense compactly generated subgroups
[EN] A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood U of the identity element of G has countably many translates xU that cover G,...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/82022 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/82022 |
| Access Level: | acceso abierto |
| Palabra clave: | Topological group Compactly generated group Dense subgroup Almost metrizable group ℵ0-bounded group Paracompact p-space Metric space σ-compact space Space of countable type |
| Sumario: | [EN] A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood U of the identity element of G has countably many translates xU that cover G, and (iv) finitely generated modulo open sets if for every non-empty open subset U of G there exists a finite set F such that F U algebraically generates G. We prove that: (1) a topological group containing a dense compactly generated subgroup is both 0-bounded and finitely generated modulo open sets, (2) an almost metrizable topological group has a dense compactly generated subgroup if and only if it is both 0-bounded and finitely generated modulo open sets, and (3) an almost metrizable topological group is compactly generated if and only if it is -compact and finitely generated modulo open sets. |
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