The isometry group of the Urysohn space as a Lévy group

DOI10.1016/j.topol.2006.02.010zbMath1127.22001arXivmath/0509402OpenAlexW2039895790MaRDI QIDQ886313

Vladimir G. Pestov

Publication date: 26 June 2007

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509402

zbMATH Keywords

isometry groupconcentration of measureUrysohn metric spaceLévy groupapproximation with finite groups

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Complete metric spaces (54E50) Means on groups, semigroups, etc.; amenable groups (43A07) Groups as automorphisms of other structures (22F50) Probabilistic metric spaces (54E70)

Related Items (13)

A universality result for endomorphism monoids of some ultrahomogeneous structures ⋮ Equivariant concentration in topological groups ⋮ Concentration of maps and group actions ⋮ Concentration of invariant means and dynamics of chain stabilizers in continuous geometries ⋮ On subgroups of minimal topological groups ⋮ Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space ⋮ Dense locally finite subgroups of automorphism groups of ultraextensive spaces ⋮ The Ramsey property for operator spaces and noncommutative Choquet simplices ⋮ The dynamical hierarchy for Roelcke precompact Polish groups ⋮ Structural Ramsey theory of metric spaces and topological dynamics of isometry groups ⋮ Concentration of $1$-Lipschitz maps into an infinite dimensional $\ell ^p$-ball with the $\ell ^q$-distance function ⋮ Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups ⋮ The Urysohn sphere is oscillation stable

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