منابع مشابه
Constructive Urysohn Universal Metric Space
We construct the Urysohn metric space in constructive setting without choice principles. The Urysohn space is a complete separable metric space which contains an isometric copy of every separable metric space, and any isometric embedding into it from a finite subspace of a separable metric space extends to the whole domain.
متن کاملOscillation Stability of the Urysohn Metric Space
We outline general concepts of oscillation stability and distortion for spaces with action of a topological transformation group, and survey a number of examples. We observe that the universal Urysohn metric space U (viewed as a homogeneous factor-space of its group of isometries) is oscillation stable, that is, for every bounded uniformly continuous function f : U → R and each ε > 0 there is a...
متن کاملThe Urysohn universal metric space and hyperconvexity
In this paper we prove that Urysohn univeral space is hyperconvex. We also examine the Gromov hyperbolicity and hyperconvexity of metric spaces. Using fourpoint property, we give a proof of the fact that hyperconvex hull of a δ-Gromov hyperbolic space is also δ-Gromov hyperbolic.
متن کاملExtension and reconstruction theorems for the Urysohn universal metric space
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
متن کاملRandom Metric Spaces and the Universal Urysohn Space.2
We introduce a model of the set of all Polish (=separable complete metric) spaces which is the cone R of distance matrices, and consider the geometrical and probabilistic problems connected with this object. We prove that the generic Polish space in the sense of this model is the so called universal Urysohn space which was defined by P.S.Urysohn in the 1920-th. Then we consider the metric space...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13511