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Products and countable dense homogeneity (1307.0184v3)
Published 30 Jun 2013 in math.GN
Abstract: Building on work of Baldwin and Beaudoin, assuming Martin's Axiom, we construct a zero-dimensional separable metrizable space $X$ such that $X$ is countable dense homogeneous while $X2$ is not. It follows from results of Hru\v{s}\'ak and Zamora Avil\'es that such a space $X$ cannot be Borel. Furthermore, $X$ can be made homogeneous and completely Baire as well.