Finitely approximable groups and actions Part I: The Ribes--Zalesski\uı property

Details Finitely approximable groups and actions Part I: The Ribes--Zalesski\uı property Finitely approximable groups and actions Part I: The Ribes--Zalesski\uı property

2007-11-08

arxiv.org/abs/0711.1362v2

Mathematics

Logic

Scientific paper

We investigate extensions of S. Solecki's theorem on closing off finite partial isometries of metric spaces \cite{solecki1} and obtain the following exact equivalence: any action of a discrete group $\Gamma$ by isometries of a metric space is finitely approximable if and only if any product of finitely generated subgroups of $\Gamma$ is closed in the profinite topology on $\Gamma$.

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