On the cardinality of countable dense homogeneous spaces

@inproceedings{Arhangelskii2013OnTC,
  title={On the cardinality of countable dense homogeneous spaces},
  author={Alexander V. Arhangel’skii and Jan van Mill},
  year={2013}
}
We prove that a countable dense homogeneous space has size at most continuum. If moreover it is compact, then it is first-countable under the Continuum Hypothesis. We also construct under the Continuum Hypothesis an example of a hereditarily separable, hereditarily Lindelof, countable dense homogeneous compact space of uncountable weight. 

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