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Keywords:
Urysohn space; bilipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem
Urysohn space; bilipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem
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.
References:
[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 http://arxiv.org/abs/math/0510120
[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
[3] Kojman, M., Shelah, S.: Almost isometric embeddings between metric spaces. Israel J. Math. 155 (2006), 309-334. DOI 10.1007/BF02773958 | MR 2269433
[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. DOI 10.4064/dm435-0-1 | MR 2232733 | Zbl 1114.57023
[5] Uspenskij, V.: The Urysohn universal metric space is homeomorphic to a Hilbert space. Topology Appl. 139 (2004), 145-149. DOI 10.1016/j.topol.2003.09.008 | MR 2051102 | Zbl 1062.54036
[6] Urysohn, P. S.: Sur un espace métrique universel I, II. Bull. Sci. Math. 51 (1927), 43-64, 74-90.
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