A rigid Urysohn-like metric space
Logic
2018-07-17 v2 General Topology
Abstract
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 extends to an automorphism of . We construct a graph of the smallest uncountable cardinality which has the same extension property as , yet its group of automorphisms is trvial. We also present a similar, although technically more complicated, construction of a complete metric space of density , having the extension property like the Urysohn space, yet again its group of isometries is trivial. This improves a recent result of Bielas.
Cite
@article{arxiv.1511.09322,
title = {A rigid Urysohn-like metric space},
author = {Jan Grebík},
journal= {arXiv preprint arXiv:1511.09322},
year = {2018}
}