On the cardinality of countable dense homogeneous spaces

Arhangel’skii, A.; van Mill, J.

doi:10.1090/S0002-9939-2013-11649-7

On the cardinality of countable dense homogeneous spaces
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by A. V. Arhangel’skii and J. van Mill PDF

Proc. Amer. Math. Soc. 141 (2013), 4031-4038 Request permission

Abstract:

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 Lindelöf, countable dense homogeneous compact space of uncountable weight.

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