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On the cardinality of countable dense homogeneous spaces


Authors: A. V. Arhangel’skii and J. van Mill
Journal: Proc. Amer. Math. Soc. 141 (2013), 4031-4038
MSC (2010): Primary 54A25, 54D65, 54H11
DOI: https://doi.org/10.1090/S0002-9939-2013-11649-7
Published electronically: July 11, 2013
MathSciNet review: 3091794
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

A. V. Arhangel’skii
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: arhangel.alex@gmail.com

J. van Mill
Affiliation: Department of Mathematics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081$^{a}$, 1081 HV Amsterdam, The Netherlands
Email: j.van.mill@vu.nl

DOI: https://doi.org/10.1090/S0002-9939-2013-11649-7
Keywords: Countable dense homogeneous, cardinality, Continuum Hypothesis
Received by editor(s): December 16, 2011
Received by editor(s) in revised form: January 10, 2012
Published electronically: July 11, 2013
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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