可磨光子群的复杂性类
Complexity classes of Polishable subgroups
摘要：
在本文中，我们进一步发展的理论规范近似的Polishable子群的波兰群体，建立在以前的工作Solecki和法拉-Solecki。特别是，我们得到了这样的典型的近似在他们的博雷尔复杂性类的一个特征。作为一个应用程序，我们提供了一个完整的列表，所有可能的Borel复杂性类的Polishable子群的波兰集团，或等价地，范围内的连续群同态之间的波兰集团。我们还提供了一个完整的列表，所有可能的博雷尔复杂性类的范围：连续群同态之间的非阿基米德波兰群体;连续线性映射之间的可分Fréchet空间;连续线性映射之间的可分巴拿赫空间。
英文摘要：
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.
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