The linear isometry group of the Gurarij space is universal

Itaï Ben Yaacov (1)

1 ICJ - Institut Camille Jordan

We give a positive answer to a question of Uspenskij, whether the linear isometry group of the Gurarij space $\bG$ is a universal Polish group. In doing so, we also give a Katětov-style construction of the Gurarij space, via a generalisation of the Arens-Eells space to metric space with a distinguished normed subspace.

Mots clés: Gurarij space; universal Polish group; Arens-Eells space

Domaines: Logique [math.LO]

Itaï Ben Yaacov. The linear isometry group of the Gurarij space is universal. 2012. ⟨hal-00681419v1⟩