The oscillation stability problem for the Urysohn sphere: A combinatorial approach

Details The oscillation stability problem for the Urysohn sphere: A combinatorial approach The oscillation stability problem for the Urysohn sphere: A combinatorial approach

2007-06-09

arxiv.org/abs/0706.1326v3

Mathematics

Metric Geometry

19 pages

Scientific paper

We study the oscillation stability problem for the Urysohn sphere, an analog
of the distortion problem for $\ell_2$ in the context of the Urysohn space
$\Ur$. In particular, we show that this problem reduces to a purely
combinatorial problem involving a family of countable ultrahomogeneous metric
spaces with finitely many distances.

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