On topological groups with a weak q-point
[EN] In this article, firstly, we introduce the concepts of weak q-spaces and weak sq-spaces. Some properties of these spaces are discussed. Secondly, we study weak q-spaces and weak sq-spaces in topological groups in terms of preimages of submetrizable spaces. We show that a topological group G is...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| 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:10251/227661 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/227661 |
| Access Level: | acceso abierto |
| Palabra clave: | Weak q-spaces Weak sq-spaces Topological groups Coset spaces Submetrizable spaces |
| Sumario: | [EN] In this article, firstly, we introduce the concepts of weak q-spaces and weak sq-spaces. Some properties of these spaces are discussed. Secondly, we study weak q-spaces and weak sq-spaces in topological groups in terms of preimages of submetrizable spaces. We show that a topological group G is a weak q-space (resp., weak sq-space) if and only if it is an open countable-compact (resp., sequential-compact) preimage of a submetrizable space.Finally, we give some characterizations of weakly feathered, weak q-spaces and weak sq-spaces in topological groups in coset spaces as follows:(1) Let H be a closed neutral subgroup of a topological group G. Then G/H is weakly feathered if and only if G/H is an open perfect preimage of a submetrizable space.(2) Let H be a closed neutral subgroup of a topological group G. Then G/H is a weak q-space (resp., weak sq-space) if and only if G/H is an open countable-compact (resp., sequential-compact) preimage of a submetrizable space. |
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