Resumen de 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.