The Urysohn universal metric space is homeomorphic to a Hilbert space

Topology and its Applications

Volumn 139, Issue 1-3, 2004, Pages 145-149

  Uspenskij, Vladimir ^a  

^a OHIO UNIVERSITY   (United States)

Author keywords

Absolute retract; Discrete approximation property; Homotopically trivial; Polish space; Toru czyk's criterion

Indexed keywords

EID: 1842606485     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2003.09.008     Document Type: Article

References (18)

1. Bogatyi S.A. Compact homogeneity of Uryson's universal metric space Uspekhi Mat. Nauk 55 2 2000 131-132 (in Russian); English translation in Russian Math. Surveys 55 2 2000 332-333
2. Bogatyi S.A. Metrically homogeneous spaces Uspekhi Mat. Nauk 57 2 2002 3-22 (in Russian); English translation in Russian Math. Surveys 57 2 2002 221-240
3. Katětov M. On universal metric spaces, in: Frolík Z. (Ed.), General Topology and its Relations to Modern Analysis and Algebra VI: Proceedings of the Sixth Prague Topological Symposium 1986 1988 323-330 Heldermann Berlin
4. Kechris A.S. Pestov V.G. Todorcevic S. Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups math.LO/0305241
5. van Mill J. Infinite-Dimensional Topology: Prerequisites and Introduction 1989 North-Holland Amsterdam
6. Bestvina M. Bowers P. Mogilski J. Walsh J. Characterization of Hilbert space manifolds revisited Topology Appl. 24 1986 53-69
7. Pestov V. Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups Israel J. Math. 127 2002 317-357 math.FA/0004010
8. Toruńczyk H. Characterizing Hilbert space topology Fund. Math. 111 3 1981 247-262
9. Urysohn P. Sur un espace métrique universel C. R. Acad. Sci. Paris 180 1925 803-806
10. Urysohn P. Sur un espace métrique universel Bull. Sci. Math. 51 1927 43-64 and 74-90
11. Uspenskij V. On the group of isometries of the Urysohn universal metric space Comment. Math. Univ. Carolin. 31 1 1990 181-182
12. Uspenskij V. On subgroups of minimal topological groups math.GN/0004119
13. Uspenskij V. Compactifications of topological groups in: P. Simon (Ed.), Proceedings of the Ninth Prague Topological Symposium, Prague, August 19-25, 2001, published April 2002 by Topology Atlas (electronic publication), pp. 331-346 math.GN/0204144
14. Vershik A.M. The universal Urysohn space, Gromov's metric triples, and random metrics on the series of natural numbers, Uspekhi Matem. Nauk 53 (5) (1998) 57-64; English translation: Russian Math. Surveys 53 (5) (1998) 921-928; A.M. Vershik, Correction Uspekhi Mat. Nauk 56 5 2001 207 in translation Russian Math. Surveys 56 5 2001 1015
15. Vershik A.M. Random metric spaces and the universal Urysohn space Fundamental Mathematics Today. 10th Anniversary of the Independent Moscow University 2002 MCCME Publishers
16. Vershik A.M. Random metric space is universal Urysohn space Doklady RAN 387 6 2002 1-4
17. Vershik A.M. Random and universal metric spaces math.PR/0205086
18. Vershik A.M. Distance matrices, random metrics and Urysohn space math.GT/0203008