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arXiv · 0711.1362

Finitely approximable groups and actions Part I: The Ribes--Zalesski\u\i{} property

Christian Rosendal
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Abstract

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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Christian Rosendal. 2007-11-08. Finitely approximable groups and actions Part I: The Ribes--Zalesski\u\i{} property. https://arxiv.org/abs/0711.1362

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