The Urysohn Sphere Is Oscillation Stable

The Urysohn Sphere Is Oscillation Stable

We solve the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ 2 in the context of the Urysohn space U . This is achieved by solving a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distance...

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Veröffentlicht in:Geometric and functional analysis 2009-09, Vol.19 (2), p.536-557
Hauptverfasser: Van Thé, Lionel Nguyen, Sauer, Norbert W.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung:We solve the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ 2 in the context of the Urysohn space U . This is achieved by solving a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-009-0007-5