A topometric Effros theorem

Itaï Ben Yaacov (1, 2) , Julien Melleray (1, 2)

1 AGL - Algèbre, géométrie, logique
2 ICJ - Institut Camille Jordan

Given a continuous and isometric action of a Polish group $G$ on an adequate Polish topometric space $(X,\tau,\rho)$ and $x \in X$, we find a necessary and sufficient condition for $\overline{Gx}^\rho$ to be co-meagre; we also obtain a criterion that characterizes when such a point exists. This work completes a criterion established in earlier work of the authors.

Mots clés: Polish group; topometric space; Effros theorem

Domaines: Logique [math.LO]; Topologie générale [math.GN]

Itaï Ben Yaacov, Julien Melleray. A topometric Effros theorem. 2022. ⟨hal-03768991v1⟩