Abstract
We complement the characterization of the graph products of cyclic groups G(Γ,p) admitting a Polish group topology of [9] with the following result. Let G=G(Γ,p), then the following are equivalent: (i) there is a metric on Γ which induces a separable topology in which EΓ is closed;(ii) G(Γ,p) is embeddable into a Polish group;(iii) G(Γ,p) is embeddable into a non-Archimedean Polish group.We also construct left-invariant separable group ultrametrics for G=G(Γ,p) and Γ a closed graph on the Baire space, which is of independent interest.
Original language | English |
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Pages (from-to) | 281-287 |
Number of pages | 7 |
Journal | Topology and its Applications |
Volume | 232 |
DOIs | |
State | Published - 1 Dec 2017 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier B.V.
Keywords
- Combinatorial group theory
- Descriptive set theory
- Graph products of groups
- Polish group topologies