| Title:
|
Central subsets of Urysohn universal spaces (English) |
| Author:
|
Niemiec, Piotr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
445-461 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subset $A$ of a metric space $(X,d)$ is central iff for every Katětov map $f: X \to \mathbb R$ upper bounded by the diameter of $X$ and any finite subset $B$ of $X$ there is $x\in X$ such that $f(a) = d(x,a)$ for each $a\in A \cup B$. Central subsets of the Urysohn universal space $\mathbb U$ (see introduction) are studied. It is proved that a metric space $X$ is isometrically embeddable into $\mathbb U$ as a central set iff $X$ has the collinearity property. The Katětov maps of the real line are characterized. (English) |
| Keyword:
|
Urysohn's universal space |
| Keyword:
|
ultrahomogeneous spaces |
| Keyword:
|
extensions of isometries |
| MSC:
|
54D65 |
| MSC:
|
54E50 |
| idZBL:
|
Zbl 1212.54093 |
| idMR:
|
MR2573417 |
| . |
| Date available:
|
2009-09-23T21:35:13Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134916 |
| . |
| Reference:
|
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