Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups
نویسندگان
چکیده
منابع مشابه
Ramsey–milman Phenomenon, Urysohn Metric Spaces, and Extremely Amenable Groups
In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group Iso (U) of isometries of Urysohn’s universal complete separable metric space U, equipped with the compact-open topology, acts upon an arbitrary compact space, it has a fixed point. The ...
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A topological group G is extremely amenable if every continuous action of G on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe’s result, we sh...
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Let F (X) and A(X) be respectively the free topological group and the free Abelian topological group on a Tychonoff space X. For every natural number n we denote by Fn(X) (An(X)) the subset of F (X) (A(X)) consisting of all words of reduced length ≤ n. It is well known that if a space X is not discrete, then neither F (X) nor A(X) is Fréchet-Urysohn, and hence first countable. On the other hand...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2002
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02784537