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Mathematics > Logic

arXiv:2202.01965 (math)
[Submitted on 4 Feb 2022]

Title:Complexity classes of Polishable subgroups

Authors: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 Fréchet spaces; continuous linear maps between separable Banach spaces.
Comments: 26 pages
Subjects: Logic (math.LO); Functional Analysis (math.FA); Group Theory (math.GR)
MSC classes: 54H05, 22A05 (Primary), 46B99, 46A04 (Secondary)
Cite as: arXiv:2202.01965 [math.LO]
  (or arXiv:2202.01965v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2202.01965

Submission history

From: Martino Lupini [view email]
[v1] Fri, 4 Feb 2022 04:26:15 UTC (812 KB)
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