Complexity classes of Polishable subgroups

Martino Lupini

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arXiv · 2202.01965

Complexity classes of Polishable subgroups

Martino Lupini

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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 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 Fr\'{e}chet spaces; continuous linear maps between separable Banach spaces.

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BibTeX RIS

Martino Lupini. 2022-02-04. Complexity classes of Polishable subgroups. https://arxiv.org/abs/2202.01965

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