Countable dense homogeneity and the Cantor set

Abstract

It is shown that CH implies the existence of a compact Hausdorff space that is countable dense homogeneous, crowded and does not contain topological copies of the Cantor set. This contrasts with a previous result by the author which says that for any crowded Hausdorff space $X$ of countable $\pi$-weight, if ${}^{\omega }X$ is countable dense homogeneous, then $X$ must contain a topological copy of the Cantor set.

References in corpus (1)

• Countable dense homogeneity of definable spaces