Extension and reconstruction theorems for the Urysohn universal metric space
Wiesław Kubiś; Matatyahu Rubin
Czechoslovak Mathematical Journal (2010)
- Volume: 60, Issue: 1, page 1-29
- ISSN: 0011-4642
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topKubiś, Wiesław, and Rubin, Matatyahu. "Extension and reconstruction theorems for the Urysohn universal metric space." Czechoslovak Mathematical Journal 60.1 (2010): 1-29. <http://eudml.org/doc/37985>.
@article{Kubiś2010,
abstract = {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.},
author = {Kubiś, Wiesław, Rubin, Matatyahu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Urysohn space; bilipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem; Urysohn space; bi-Lipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem},
language = {eng},
number = {1},
pages = {1-29},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extension and reconstruction theorems for the Urysohn universal metric space},
url = {http://eudml.org/doc/37985},
volume = {60},
year = {2010},
}
TY - JOUR
AU - Kubiś, Wiesław
AU - Rubin, Matatyahu
TI - Extension and reconstruction theorems for the Urysohn universal metric space
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 1
EP - 29
AB - 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.
LA - eng
KW - Urysohn space; bilipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem; Urysohn space; bi-Lipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem
UR - http://eudml.org/doc/37985
ER -
References
top- 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.
- Huhunaišvili, G. E., On a property of Uryson's universal metric space, Dokl. Akad. Nauk SSSR (N.S.) 101 (1955), 607-610 Russian. (1955) MR0072454
- Kojman, M., Shelah, S., 10.1007/BF02773958, Israel J. Math. 155 (2006), 309-334. (2006) MR2269433DOI10.1007/BF02773958
- Yomdin, M. Rubin,Y., 10.4064/dm435-0-1, Dissertationes Math. 435 (2005), 1-246. (2005) Zbl1114.57023MR2232733DOI10.4064/dm435-0-1
- Uspenskij, V., 10.1016/j.topol.2003.09.008, Topology Appl. 139 (2004), 145-149. (2004) Zbl1062.54036MR2051102DOI10.1016/j.topol.2003.09.008
- Urysohn, P. S., Sur un espace métrique universel I, II, Bull. Sci. Math. 51 (1927), 43-64, 74-90. (1927)
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