论文标题
可抛光亚组的复杂性类别
Complexity classes of Polishable subgroups
论文作者
论文摘要
在本文中，我们进一步发展了波兰群体可波兰人亚组的规范近似理论，这些理论是基于Solecki和Farah-Solecki的先前工作的。特别是，我们从其borel复杂性类别方面获得了这种规范近似的表征。作为一个应用程序，我们提供了波兰人群体的可波兰人亚组的所有可能的Borel复杂性类别的完整列表，或者等效地列出了波兰群体之间连续组同构范围的范围。我们还提供了以下范围的所有可能的Borel复杂性类别的完整列表：非Archimedean波兰群体之间的连续群体同态；可分离的弗雷切特空间之间的连续线性图；可分离的Banach空间之间的连续线性图。
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.
