Work

Complexity classes of Polishable subgroups

Year: 2025

Type: article

Abstract: 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 complete characterization of the Borel complexity class of a Polishable subgroup in terms of its canonical approximation. 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; and continuous linear maps between separable Banach spaces.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1605

Author: Martino Lupini

Institution: University of Bologna

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Royal Society Te Apārangi, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, Marsden Fund

Awards: G1290427602, G2735103206