Isometry of Polish metric spaces
نویسندگان
چکیده
منابع مشابه
Isometry of Polish metric spaces
We consider the equivalence relation of isometry of separable, complete metric spaces, and show that any equivalence relation induced by a Borel action of a Polish group on a Polish space is Borel reducible to this isometry relation. We also consider the isometry relation restricted to various classes of metric spaces, and produce lower bounds for the complexity in terms of the Borel reducibili...
متن کاملOn the classification of Polish metric spaces up to isometry
(A) A Polish metric space is a complete separable metric space (X, d). Our first goal in this paper is to determine the exact complexity of the classification problem of Polish metric spaces up to isometry. Our work was motivated by a recent paper of Vershik [1998], where the author remarks (in the beginning of Section 2): “The classification of Polish spaces up to isometry is an enormous task....
متن کاملIsometry Groups of Separable Metric Spaces
We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base a...
متن کاملPolish ultrametric Urysohn spaces and their isometry groups
Article history: Received 15 July 2009 Received in revised form 2 December 2010 Accepted 5 December 2010
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: Annals of Pure and Applied Logic
سال: 2012
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.01.001