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Finitely approximate groups and actions Part I: The Ribes–Zalesskiĭ property

Published online by Cambridge University Press:  12 March 2014

Christian Rosendal
Christian Rosendal*
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinoisat Chicago, 851 S. Morgan St., Chicago, IL 60607-7045, USA, E-mail: rosendal.math@gmail.com, URL: http://www.math.uic.edu/~rosendal
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Abstract

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.

Keywords

Urysohn metric spaceprofinite topologythe Ribes–Zalesskiĭ Theorem
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1297 - 1306
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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