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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Detalles Bibliográficos
Autor: Druzhinina, Irina
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
Descripción
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.