A rigid Urysohn-like space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00475626" target="_blank" >RIV/67985840:_____/17:00475626 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/proc/13511" target="_blank" >http://dx.doi.org/10.1090/proc/13511</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/13511" target="_blank" >10.1090/proc/13511</a>
Alternative languages
Result language
angličtina
Original language name
A rigid Urysohn-like space
Original language description
Recall that the Rado graph is the unique countable graph that realizes all one-point extensions of its finite subgraphs. The Rado graph is well known to be universal and homogeneous in the sense that every isomorphism between finite subgraphs of $R$ extends to an automorphism of $R$. We construct a graph of the smallest uncountable cardinality $omega _1$ which has the same extension property as $R$, yet its group of automorphisms is trivial. We also present a similar, although technically more complicated, construction of a complete metric space of density $omega _1$, having the extension property like the Urysohn space, yet again its group of isometries is trivial. This improves a recent result of Bielas.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
145
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
4049-4060
UT code for WoS article
000404113200036
EID of the result in the Scopus database
2-s2.0-85021424701