2022/02/04 by Martino Lupini, Lupini, Martino
Mathematics · #22A05 (Primary) #46A04 (Secondary) #46B99 #54H05 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2202.01965
openalex publication_date 2022/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we further develop the theory of canonical approximations of Polishable subgroups of Polish groups, building on previous work of Solecki and Farah--Solecki. In particular, we obtain a characterization of such canonical approximations in terms of their Borel complexity class. As an application we provide a complete list of all the possible Borel complexity classes of Polishable subgroups of Polish groups or, equivalently, of the ranges of continuous group homomorphisms between Polish groups. We also provide a complete list of all the possible Borel complexity classes of the ranges of: continuous group homomorphisms between non-Archimedean Polish groups; continuous linear maps between separable Fréchet spaces; continuous linear maps between separable Banach spaces.