Countable dense homogeneous filters and the Menger covering property

Abstract

In this note 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 a metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.

8 pages

References in corpus (1)

• A remark on Fremlin-Miller theorem concerning the Menger property and Michael concentrated sets

Cited by in corpus (1)

• Coideals as remainders of groups distinguishing between combinatorial covering properties