Connected metrizable subtopologies and partitions into copies of the Cantor set

Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)

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1919-6026-1-PB.pdf (196.75 KB)

Fecha

2006-10-01

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https://riunet.upv.es/handle/10251/82988

Cita bibliográfica

Druzhinina, I. (2006). Connected metrizable subtopologies and partitions into copies of the Cantor set. Applied General Topology. 7(2):139-150. https://doi.org/10.4995/agt.2006.1919

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Resumen

[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.

Palabras clave

Metrizable space, Completely metrizable space, Condensation, Connected metrizable subtopology, Cantor se, Zero-dimensional space, Martin’s Axiom

Fuente

Applied General Topology issn: 1576-9402

DOI

10.4995/agt.2006.1919

Versión del editor

https://doi.org/10.4995/agt.2006.1919

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Applied General Topology - Vol 07, No 2 (2006)