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Countable dense homogeneity and the Cantor set

Volume 246 / 2019

Rodrigo Hernández-Gutiérrez Fundamenta Mathematicae 246 (2019), 45-70 MSC: Primary 54G20; Secondary 54D65, 54D30, 54B35. DOI: 10.4064/fm571-5-2018 Published online: 11 January 2019


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.


  • Rodrigo Hernández-GutiérrezDepartamento de Matemáticas
    Universidad Autónoma Metropolitana campus Iztapalapa
    Av. San Rafael Atlixco 186
    Col. Vicentina, Iztapalapa
    09340, Mexico City, Mexico

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