The isometry group of the Urysohn space as a Lévy group
TLDR
The isometry group Iso (U ) of the universal Urysohn metric space U equipped with the natural Polish topology is a Levy group in the sense of Gromov and Milman, that is, admits an approximating chain of compact subgroups as discussed by the authors.About:
This article is published in Topology and its Applications.The article was published on 2007-05-15 and is currently open access. It has received 31 citations till now. The article focuses on the topics: Isometry group & Urysohn and completely Hausdorff spaces.read more
Citations
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On subgroups of minimal topological groups
TL;DR: A topological group is a subgroup of a minimal topologically simple Roelcke-precompact group of the form Iso (M ), where M is an appropriate non-separable version of the Urysohn space as discussed by the authors.
Journal ArticleDOI
A topological version of the Bergman property
TL;DR: In this paper, a topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits.
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Structural Ramsey theory of metric spaces and topological dynamics of isometry groups
TL;DR: In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces is closely related to the combinatorial behavior of the class of their finite metric spaces.
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A topological version of the Bergman property
TL;DR: In this paper, a topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits.
References
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Book
Metric Structures for Riemannian and Non-Riemannian Spaces
TL;DR: In this paper, Loewner proposed a metric structure with a bounded Ricci Curvature for length structures on families of metric spaces, where the degree and dilatation of the length structure is a function of degree and degree.
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The concentration of measure phenomenon
TL;DR: Concentration functions and inequalities isoperimetric and functional examples Concentration and geometry Concentration in product spaces Entropy and concentration Transportation cost inequalities Sharp bounds of Gaussian and empirical processes Selected applications References Index
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Combinatorial Group Theory.
Book
Asymptotic theory of finite dimensional normed spaces
Vitali Milman,Gideon Schechtman +1 more
TL;DR: The concentration of measure phenomenons in the theory of Normed spaces was discussed in this paper, where the Rademacher projection was applied to the case of finite Dimensional Normed Spaces.
Journal ArticleDOI
A topological application of the isoperimetric inequality
VD Milman,M Gromov +1 more