Countable dense homogeneous filters and the Menger covering property
Tom 224 / 2014
Fundamenta Mathematicae 224 (2014), 233-240
MSC: Primary 54D20; Secondary 54D80, 22A05.
DOI: 10.4064/fm224-3-3
Streszczenie
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.
