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arXiv · 1406.0692

Countable dense homogeneous filters and the Menger covering property

Dušan Repovš·Lyubomyr Zdomskyy·Shuguo Zhang
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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 Hern\'andez-Guti\'errez and Hru\v{s}\'ak. 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.

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Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang. 2014-06-03. Countable dense homogeneous filters and the Menger covering property. https://doi.org/10.4064/fm224-3-3

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