| 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:
|
http://hdl.handle.net/10338.dmlcz/140544 |
| . |
| 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 http://arxiv.org/abs/math/0510120. |
| 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. |
| . |
