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Finitely Approximable Groups and Actions Part I: the Ribes-Zalesskii Property

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journal contribution
posted on 2012-03-16, 00:00 authored by Christian Rosendal
We investigate extensions of S. Solecki’s theorem on closing off finite partial isometries of metric spaces [11] and obtain the following exact equivalence: any action of a discrete group Γ by isometries of a metric space is finitely approximable if and only if any product of finitely generated subgroups of Γ is closed in the profinite topology on Γ.

Funding

The author was partially supported by NSF grants DMS 0901405 and DMS 0919700. The author is also grateful for the helpful suggestions of the anonymous referee.

History

Publisher Statement

The original version is available through Association for Symbolic Logic at DOI:10.2178/jsl/1318338850

Publisher

Association for Symbolic Logi

Language

  • en_US

issn

0022-4812

Issue date

2011-01-01

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