The Urysohn sphere is oscillation stable
L. Nguyen Van Th\'e, N. W. Sauer
TL;DR
This paper proves the oscillation stability of the Urysohn sphere by solving a combinatorial problem related to countable homogeneous metric spaces with finitely many distances.
Contribution
It introduces a novel combinatorial approach to establish the oscillation stability of the Urysohn sphere, extending the understanding of universal metric spaces.
Findings
Urysohn sphere is oscillation stable
Solved a combinatorial problem for countable homogeneous metric spaces
Extended stability results to universal metric spaces
Abstract
We solve the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for the Hilbert space in the context of the Urysohn universal metric space. This is achieved by solving a purely combinatorial problem involving a family of countable homogeneous metric spaces with finitely many distances.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Advanced Operator Algebra Research