Geometry in Urysohn's universal metric space
| dc.creator | Melleray, Julien | |
| dc.date | 2005-05-24 | |
| dc.date | 2005-06-22 | |
| dc.date.accessioned | 2026-07-07T05:20:14Z | |
| dc.date.available | 2026-07-07T05:20:14Z | |
| dc.description | Recently, much interest was devoted to the Urysohn universal metric space U and its isometries; this paper is a contribution to this field of research. In particular, we study some properties of isometries of U, and prove the following result, which answers a question of Urysohn: if X is a subset of U is such that, for any X' which is isometric to X there exists an isometry of U which maps X to X', then X is compact (the converse was already well-known). We also answer in the negative a question of Clemens, proving that any Polish metric space is isometric to the set of fixed points of some isometry of U. | |
| dc.description | v2: corrected some grammatical errors and typos, and added a part dealing with properties of the sets of fixed points of isometries | |
| dc.identifier | https://arxiv.org/abs/math/0505508 | |
| dc.identifier | http://arxiv.org/abs/math/0505508 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75302 | |
| dc.subject | Metric Geometry | |
| dc.subject | 51F (primary) 99 (secondary) | |
| dc.title | Geometry in Urysohn's universal metric space | |
| dc.type | text |