Title: 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.