The Urysohn sphere is oscillation stable

Details The Urysohn sphere is oscillation stable The Urysohn sphere is oscillation stable

2007-10-15

arxiv.org/abs/0710.2884v3

Mathematics

Metric Geometry

21 pages, 1 figure. This is the post-last version of the paper. A mistake had to be fixed in the article by Lopez-Abad and Ngu

Scientific paper

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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