English

Countable dense homogeneity and the Cantor set

General Topology 2020-01-20 v1

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 XX of countable π\pi-weight, if ωX{}^\omega{X} is countable dense homogeneous, then XX must contain a topological copy of the Cantor set.

Keywords

Cite

@article{arxiv.1705.01203,
  title  = {Countable dense homogeneity and the Cantor set},
  author = {Rodrigo Hernández-Gutiérrez},
  journal= {arXiv preprint arXiv:1705.01203},
  year   = {2020}
}
R2 v1 2026-06-22T19:34:59.940Z