# Countable Dense Homogeneity and the Double Arrow Space

@inproceedings{HernndezGutirrez2013CountableDH,
title={Countable Dense Homogeneity and the Double Arrow Space},
author={Rodrigo Hern{\'a}ndez-Guti{\'e}rrez},
year={2013}
}
Let $\mathbb{A}$ denote the Alexandroff-Urysohn double arrow space. We prove the following results: (a) $\mathbb{A}\times{}^\omega{2}$ is not countable dense homogeneous; (b) ${}^{\omega}{\mathbb{A}}$ is not countable dense homogeneous; (c) $\mathbb{A}$ has exactly $\mathfrak{c}$ types of countable dense subsets. These results answer questions by Arhangel'ski\u\i, Hru\v{s}\'ak and van Mill.

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