Countable dense homogeneity and the Cantor set

摘要

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 X-omega is countable dense homogeneous, then X must contain a topological copy of the Cantor set.