The dynamical hierarchy for Roelcke precompact Polish groups

2014/05/19 by Tomás Ibarlucía, Ibarlucía, Tomás · 8 citations
Mathematics · #Advanced Topology and Set Theory #Geometric and Algebraic Topology #Mathematics and Applications

paper · doi:10.1007/s11856-016-1399-1

Abstract

We study several distinguished function algebras on a Polish group G, under the assumption that G is Roelcke precompact. We do this by means of the model-theoretic translation initiated by Ben Yaacov and Tsankov: we investigate the dynamics of ℵ₀-categorical metric structures under the action of their automorphism group. We show that, in this context, every strongly uniformly continuous function (in particular, every Asplund function) is weakly almost periodic. We also point out the correspondence between tame functions and NIP formulas, deducing that the isometry group of the Urysohn sphere is \Tame∩\UC-trivial.

Citations

• New algebras of functions on topological groups arising from G-spaces

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