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

2007/06/09 by J. López-Abad, Abad, Jordi Lopez, Lionel Nguyen Van Thé +1 · 1 citation
Mathematics · #22F05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.0706.1326

openalex publication_date 2007/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ₂ 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.

Citations

• The distortion problem

Cited by

• Oscillating subalgebras of the atomless countable Boolean algebra

Related

• Oscillation stability of the Urysohn metric space
• Oscillation stability by the Carlson-Simpson theorem
• Oscillation of Urysohn type spaces
• The Urysohn sphere is pseudofinite
• Definable Functions in Urysohn's Metric Space