Geodesic
Countable dense homogeneous filters and the Menger covering property
Dušan Repovš1 ; Lyubomyr Zdomskyy2 ; Shuguo Zhang3
1 Faculty of Education, and Faculty of Mathematics and Physics University of Ljubljana P.O. Box 2964 Ljubljana, Slovenia 1001
2 Kurt Gödel Research Center for Mathematical Logic University of Vienna Währinger Straße 25, A-1090 Wien, Austria
3 College of Mathematics Sichuan University Chengdu, Sichuan 610064, China
Fundamenta Mathematicae, Tome 224 (2014) no. 3, pp. 233-240.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm224-3-3
Keywords: present zfc construction non meager filter which fails countable dense homogeneous answers question hern ndez guti rrez hru method proof allows obtain omega cup infty n dimensional metrizable baire topological group which strongly locally homogeneous countable dense homogeneous

Dušan Repovš 1 ; Lyubomyr Zdomskyy 2 ; Shuguo Zhang 3

1 Faculty of Education, and Faculty of Mathematics and Physics University of Ljubljana P.O. Box 2964 Ljubljana, Slovenia 1001
2 Kurt Gödel Research Center for Mathematical Logic University of Vienna Währinger Straße 25, A-1090 Wien, Austria
3 College of Mathematics Sichuan University Chengdu, Sichuan 610064, China 
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Dušan Repovš; Lyubomyr Zdomskyy; Shuguo Zhang. Countable dense homogeneous filters and
 the Menger covering property. Fundamenta Mathematicae, Tome 224 (2014) no. 3, pp. 233-240. doi : 10.4064/fm224-3-3. http://geodesic.mathdoc.fr/articles/10.4064/fm224-3-3/

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