Journal of Symbolic Logic

Finitely approximable groups and actions Part I: The Ribes—Zaluesskiĭ 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 [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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 4 (2011), 1297-1306.

Dates
First available in Project Euclid: 11 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1318338850

Digital Object Identifier
doi:10.2178/jsl/1318338850

Mathematical Reviews number (MathSciNet)
MR2895386

Zentralblatt MATH identifier
1250.03085

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]

Keywords
Urysohn metric space profinite topology the Ribes—Zalesskiĭ Theorem

Citation

Rosendal, Christian. Finitely approximable groups and actions Part I: The Ribes—Zaluesskiĭ property. J. Symbolic Logic 76 (2011), no. 4, 1297--1306. doi:10.2178/jsl/1318338850. https://projecteuclid.org/euclid.jsl/1318338850


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