A topometric Effros theorem

2022/09/06 by Itaï Ben Yaacov, Yaacov, Itaï Ben, Julien Melleray +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2209.02245

openalex publication_date 2022/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a continuous and isometric action of a Polish group G on an adequate Polish topometric space (X,τ,ρ) and x ∈ X, we find a necessary and sufficient condition for Gx^ρ 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.

Related

• Grey subsets of Polish spaces
• On the scope of the Effros theorem
• The open mapping principle for partial actions of polish groups
• Sharper changes in topologies
• Polishability of some groups of interval and circle diffeomorphisms