Geometry in Urysohn's universal metric space Export

@misc{citeulike:210416, abstract = {Recently, much interest was devoted to the Urysohn universal metric space IU and its isometries; this paper is a contribution to this field of research. In particular, we study some properties of isometries of IU, and prove the following result, which answers a question of Urysohn: if X is a subset of IU is such that, for any X' which is isometric to X there exists an isometry of IU which maps X to X', then X is compact (the converse was already well-known).}, archivePrefix = {arXiv}, author = {Melleray, Julien}, citeulike-article-id = {210416}, citeulike-linkout-0 = {http://arxiv.org/abs/math.MG/0505508}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.MG/0505508}, eprint = {math.MG/0505508}, keywords = {descriptive-set-theory}, month = {May}, posted-at = {2006-10-11 17:24:35}, priority = {2}, title = {Geometry in Urysohn's universal metric space}, url = {http://arxiv.org/abs/math.MG/0505508}, year = {2005} }

TY - ELEC ID - citeulike:210416 L3 - citeulike-article-id:210416 N2 - Recently, much interest was devoted to the Urysohn universal metric space IU and its isometries; this paper is a contribution to this field of research. In particular, we study some properties of isometries of IU, and prove the following result, which answers a question of Urysohn: if X is a subset of IU is such that, for any X' which is isometric to X there exists an isometry of IU which maps X to X', then X is compact (the converse was already well-known). TI - Geometry in Urysohn's universal metric space KW - descriptive-set-theory AU - Melleray, Julien PY - 2005/05/24/ UR - http://arxiv.org/abs/math.MG/0505508 ER -