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

2007/11/08 by Christian Rosendal, Rosendal, Christian · 3 citations
Mathematics · #03C15 #03E15 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C15 #msc:03E15

paper · pdf · doi:10.48550/arxiv.0711.1362

openalex publication_date 2007/11/08 · arxiv created 2011/04/17 · arxiv updated 2011/04/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We investigate extensions of S. Solecki's theorem on closing off finite partial isometries of metric spaces \citesolecki1 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.

Cited by

• On finite local approximations of isometric actions of residually finite groups
• Isometry groups and countable groups with the Lévy property
• The Ribes-Zalesskiĭ product theorem via foldings and extensions

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