×

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 \(\Gamma\).

MSC:

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

Citations:

Zbl 1124.54012
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] DOI: 10.1142/S0218196701000449 · Zbl 1024.20022
[2] Forum Mathematician 17 pp 513– (2005)
[3] DOI: 10.1142/S0218196791000079 · Zbl 0722.20039
[4] Commentationes Mathematicae Universitatis Carotinae 31 pp 181– (1990)
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.