Agostini, C., Medini, A., & Zdomskyy, L. (2025). Countable dense homogeneity and topological groups. Topology and Its Applications, 373, Article 109537. https://doi.org/10.1016/j.topol.2025.109537
Building on results of Medvedev, we construct a ZFC example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of Z<sup>ω</sup> of size b that is a λ-set. We also conjecture that every countable dense homogeneous Baire topological group with no isolated points contains a copy of the Cantor set, and give a proof in a very special case.
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Project title:
Mengentheoretische Aspekte topologischer Auswahlprinzipien: I 5930-N (FWF - Österr. Wissenschaftsfonds) Topologische Anwendungen der Wadge-Theorie: P 35588-N (FWF - Österr. Wissenschaftsfonds) Fragen zur topologischen Homogenität: P 35655-N (FWF - Österr. Wissenschaftsfonds)
CC BY 4.0
