Finitely approximable groups and actions. I: The Ribes-Zalesskiń≠ property. (English) Zbl 1250.03085

Summary: We investigate extensions of S. Solecki’s theorem on closing off finite partial isometries of metric spaces [S. Solecki, Isr. J. Math. 150, 315–331 (2005; Zbl 1124.54012)] 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 \(\Gamma\).


03E15 Descriptive set theory
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
54H20 Topological dynamics (MSC2010)


Zbl 1124.54012
Full Text: DOI arXiv


[1] DOI: 10.1142/S0218196701000449 · Zbl 1024.20022
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[5] DOI: 10.1007/BF02762385 · Zbl 1124.54012
[6] DOI: 10.1090/S0002-9947-1949-0032642-4
[7] Finitely approximable groups and actions. Part II: Generic representations 76 pp 1307– (2011) · Zbl 1250.03086
[8] DOI: 10.1112/blms/23.4.356 · Zbl 0754.20007
[9] DOI: 10.1007/BF01305233 · Zbl 0767.05053
[10] DOI: 10.1090/S0002-9947-99-02374-0 · Zbl 0947.20018
[11] DOI: 10.2307/1969513
[12] DOI: 10.1112/blms/25.1.37 · Zbl 0811.20026
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