On the geometry of Urysohn's universal metric space
TLDR
In this article, it was shown that compact homogeneity is the strongest homogeneity property possible in the Urysohn space U and its isometry group, and that any Polish metric space is isometric to the set of fixed points of some isometry φ.About:
This article is published in Topology and its Applications.The article was published on 2007-01-15 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Isometry group & Urysohn's lemma.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.
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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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Some geometric and dynamical properties of the Urysohn space
TL;DR: In this article, the authors present a survey article about the geometry and dynamical properties of the Urysohn space, which is part of the author's Ph.D. thesis.
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Completeness of the isomorphism problem for separable C*-algebras
TL;DR: In this article, it was shown that the isomorphism problem for separable (simple, AI) C*-algebras is complete in the class of orbit equivalence relations.
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Extending lipschitz maps into c(k)-spaces
TL;DR: In this paper, it was shown that if K is a compact metric space, then C(K) is a 2-absolute Lipschitz retract, and the same result holds for spaces with Gateaux smooth norm or of dimension two.
References
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Book
Classical descriptive set theory
TL;DR: In this article, the authors present a largely balanced approach, which combines many elements of the different traditions of the subject, and includes a wide variety of examples, exercises, and applications, in order to illustrate the general concepts and results of the theory.
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.
Book
The descriptive set theory of Polish group actions
TL;DR: In this paper, the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations, which is a special case of locally compact groups and has been studied in many areas of mathematics.
Book ChapterDOI
The Descriptive Set Theory of Polish Group Actions: DESCRIPTIVE SET THEORY
TL;DR: The descriptive set theory of polish group actions are a good way to achieve details about operating certain products as discussed by the authors. But they are not a good fit for the use of instruction manuals.