Work

Countable dense homogeneity and topological groups

Year: 2025

Type: article

Abstract: 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 ω 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.

Source: Topology and its Applications

DOI: 10.1016/j.topol.2025.109537

Authors: Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy

Institution: TU Wien

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,920

Funder: Austrian Science Fund