Connected metrizable subtopologies and partitions into copies of the Cantor set

Irina Druzhinina


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.


Metrizable space; Completely metrizable space; Condensation; Connected metrizable subtopology; Cantor set; Zero-dimensional space; Martin’s Axiom

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