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Countable dense homogeneous filters and the Menger covering property

Volume 224 / 2014

Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang Fundamenta Mathematicae 224 (2014), 233-240 MSC: Primary 54D20; Secondary 54D80, 22A05. DOI: 10.4064/fm224-3-3


We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any $n\in \omega \cup \{\infty \}$ an $n$-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.


  • Dušan RepovšFaculty of Education, and
    Faculty of Mathematics and Physics
    University of Ljubljana
    P.O. Box 2964 Ljubljana, Slovenia 1001
  • Lyubomyr ZdomskyyKurt Gödel Research Center for
    Mathematical Logic
    University of Vienna
    Währinger Straße 25, A-1090 Wien, Austria
  • Shuguo ZhangCollege of Mathematics
    Sichuan University
    Chengdu, Sichuan 610064, China

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