Connected metrizable subtopologies and partitions into copies of the Cantor set
[EN] We prove under Martin’s Axiom that every separable metrizable space represented as the union of less than 2 ω zero-dimensional compact subsets is zero-dimensional. On the other hand, we show in ZFC that every separable completely metrizable space without isolated points is the union of 2ω pairw...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2006 |
| 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:10251/82988 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/82988 |
| Access Level: | acceso abierto |
| Palabra clave: | Metrizable space Completely metrizable space Condensation Connected metrizable subtopology Cantor se Zero-dimensional space Martin’s Axiom |
| Sumario: | [EN] We prove under Martin’s Axiom that every separable metrizable space represented as the union of less than 2 ω zero-dimensional compact subsets is zero-dimensional. On the other hand, we show in ZFC that every separable completely metrizable space without isolated points is the union of 2ω pairwise disjoint copies of the Cantor set. |
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