npsD839.pdf (137.25 kB)
Finitely Approximable Groups and Actions Part I: the Ribes-Zalesskii Property
journal contributionposted 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  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.
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.
Publisher StatementThe original version is available through Association for Symbolic Logic at DOI:10.2178/jsl/1318338850
PublisherAssociation for Symbolic Logi