Connected metrizable subtopologies and partitions into copies of the Cantor set

• Druzhinina, Irina ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 7, Nº. 2, 2006, págs. 139-150
• Idioma: inglés
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• Resumen

  • 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.