Mathematics – Metric Geometry
Scientific paper
2005-05-24
Mathematics
Metric Geometry
v2: corrected some grammatical errors and typos, and added a part dealing with properties of the sets of fixed points of isome
Scientific paper
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.
Melleray Julien
No associations
LandOfFree
Geometry in Urysohn's universal metric space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geometry in Urysohn's universal metric space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry in Urysohn's universal metric space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-72889