<div class="csl-bib-body">
<div class="csl-entry">Agostini, C., Medini, A., & Zdomskyy, L. (2025). Countable dense homogeneity and topological groups. <i>Topology and Its Applications</i>, <i>373</i>, Article 109537. https://doi.org/10.1016/j.topol.2025.109537</div>
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dc.identifier.issn
0166-8641
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/221405
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dc.description.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<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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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.publisher
ELSEVIER
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dc.relation.ispartof
Topology and its Applications
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Baire space
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dc.subject
Countable dense homogeneous
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dc.subject
h-Homogeneous
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dc.subject
Homogeneous
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dc.subject
Topological group
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dc.subject
λ-Set
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dc.title
Countable dense homogeneity and topological groups
