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

Jordi Lopez Abad (1) , Lionel Nguyen van Thé (1, 2)

1 ELM - Équipe de Logique Mathématique
2 University of Calgary

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.

Mots clés: Topological groups actions; Oscillation stability; Ramsey theory; Metric geometry; Urysohn metric space

Domaines: Géométrie métrique [math.MG]; Combinatoire [math.CO]

Jordi Lopez Abad, Lionel Nguyen van Thé. The oscillation stability problem for the Urysohn sphere: A combinatorial approach.. 2009. ⟨hal-00153360v3⟩