Countable dense homogeneity and topological groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910786858778624 |
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| author | Agostini, Claudio Medini, Andrea Zdomskyy, Lyubomyr |
| author_facet | Agostini, Claudio Medini, Andrea Zdomskyy, Lyubomyr |
| contents | Building on results of Medvedev, we construct a $\mathsf{ZFC}$ example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\mathbb{Z}^ω$ of size $\mathfrak{b}$ that is a $λ$-set. We also conjecture that every countable dense homogenous Baire topological group with no isolated points contains a copy of the Cantor set, and give a proof in a very special case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_09455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Countable dense homogeneity and topological groups Agostini, Claudio Medini, Andrea Zdomskyy, Lyubomyr General Topology 54H11, 54G20 Building on results of Medvedev, we construct a $\mathsf{ZFC}$ example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\mathbb{Z}^ω$ of size $\mathfrak{b}$ that is a $λ$-set. We also conjecture that every countable dense homogenous Baire topological group with no isolated points contains a copy of the Cantor set, and give a proof in a very special case. |
| title | Countable dense homogeneity and topological groups |
| topic | General Topology 54H11, 54G20 |
| url | https://arxiv.org/abs/2501.09455 |