Countable dense homogeneity and the Cantor set
Volume 246 / 2019
Fundamenta Mathematicae 246 (2019), 45-70
MSC: Primary 54G20; Secondary 54D65, 54D30, 54B35.
DOI: 10.4064/fm571-5-2018
Published online: 11 January 2019
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 $\hskip 1pt{}^ \omega {\hskip -1.5pt X}$ is countable dense homogeneous, then $X$ must contain a topological copy of the Cantor set.
