Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups
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Publication:1611548
DOI10.1007/BF02784537zbMath1007.43001arXivmath/0004010OpenAlexW2064519696MaRDI QIDQ1611548
Publication date: 26 March 2003
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0004010
Metric spaces, metrizability (54E35) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Means on groups, semigroups, etc.; amenable groups (43A07)
Related Items (32)
The Ramsey property for Banach spaces and Choquet simplices ⋮ The Urysohn universal metric space is homeomorphic to a Hilbert space ⋮ Concentration of measure, classification of submeasures, and dynamics of \(L_0\) ⋮ Some classes of minimally almost periodic topological groups ⋮ Automorphism groups of countable structures and groups of measurable functions ⋮ Equivariant concentration in topological groups ⋮ Extending partial isometries ⋮ Gowers' Ramsey theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan ⋮ Generic representations of abelian groups and extreme amenability ⋮ Concentration of maps and group actions ⋮ On amenability and groups of measurable maps ⋮ Concentration of Haar measures, with an application to random matrices ⋮ The isometry group of the Urysohn space as a Lévy group ⋮ The Polish topology of the isometry group of the infinite dimensional hyperbolic space ⋮ Ramsey properties of finite measure algebras and topological dynamics of the group of measure preserving automorphisms: Some results and an open problem ⋮ Constructions of Urysohn universal ultrametric spaces ⋮ Concentration of invariant means and dynamics of chain stabilizers in continuous geometries ⋮ Ramsey property, ultrametric spaces, finite posets, and universal minimal flows ⋮ Random orderings and unique ergodicity of automorphism groups ⋮ Extreme amenability of \(L_0\), a Ramsey theorem, and Lévy groups ⋮ A finite presentation of the rational Urysohn space ⋮ The Ramsey property for operator spaces and noncommutative Choquet simplices ⋮ Polish groups and Baire category methods ⋮ Structural Ramsey theory of metric spaces and topological dynamics of isometry groups ⋮ Extreme amenability of abelian \(L_0\) groups ⋮ Universal Flows of Closed Subgroups of S ∞ and Relative Extreme Amenability ⋮ Transitivity in spaces of vector-valued functions ⋮ A corrigendum to the article: Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups ⋮ Equivariant dissipation in non-Archimedean groups ⋮ Ramsey properties of finite posets ⋮ The Urysohn sphere is oscillation stable ⋮ Fixed points in compactifications and combinatorial counterparts
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