Previous |  Up |  Next


Title: Extension and reconstruction theorems for the Urysohn universal metric space (English)
Author: Kubiś, Wiesław
Author: Rubin, Matatyahu
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 60
Issue: 1
Year: 2010
Pages: 1-29
Summary lang: English
Category: math
Summary: We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets. (English)
Keyword: Urysohn space
Keyword: bilipschitz homeomorphism
Keyword: modulus of continuity
Keyword: reconstruction theorem
Keyword: extension theorem
MSC: 20E36
MSC: 22F50
MSC: 51F99
MSC: 54E40
MSC: 54H11
idZBL: Zbl 1224.22010
idMR: MR2595067
Date available: 2010-07-20T16:11:05Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] Fonf, V. P., Rubin, M.: Reconstruction theorem for homeomorphism groups without small sets and non-shrinking functions of a normed space.Preprint in Math Arxiv. Available at
Reference: [2] Huhunaišvili, G. E.: On a property of Uryson's universal metric space.Dokl. Akad. Nauk SSSR (N.S.) 101 (1955), 607-610 Russian. MR 0072454
Reference: [3] Kojman, M., Shelah, S.: Almost isometric embeddings between metric spaces.Israel J. Math. 155 (2006), 309-334. MR 2269433, 10.1007/BF02773958
Reference: [4] Yomdin, M. Rubin,Y.: Reconstruction of manifolds and subsets of normed spaces from subgroups of their homeomorphism groups.Dissertationes Math. 435 (2005), 1-246. Zbl 1114.57023, MR 2232733, 10.4064/dm435-0-1
Reference: [5] Uspenskij, V.: The Urysohn universal metric space is homeomorphic to a Hilbert space.Topology Appl. 139 (2004), 145-149. Zbl 1062.54036, MR 2051102, 10.1016/j.topol.2003.09.008
Reference: [6] Urysohn, P. S.: Sur un espace métrique universel I, II.Bull. Sci. Math. 51 (1927), 43-64, 74-90.


Files Size Format View
CzechMathJ_60-2010-1_1.pdf 391.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo