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arXiv · 1307.0184

Products and countable dense homogeneity

Andrea Medini
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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 $X^2$ is not. It follows from results of Hrušák and Zamora Avilés that such a space $X$ cannot be Borel. Furthermore, $X$ can be made homogeneous and completely Baire as well.

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Andrea Medini. 2014-06-10. Products and countable dense homogeneity. https://arxiv.org/abs/1307.0184

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