On the complexity of the uniform homeomorphism
relation
between separable Banach spaces
Su Gao, Steve Jackson and Bunyamin
Sari
Abstract
In this paper we investigate the uniform
homeomorphism relation between separable Banach spaces and the related relation
of local equivalence. We completely characterize the descriptive complexity of local
equivalence in the Borel reducibility hierarchy. This also provides a lower
bound for the uniform homeomorphism.
Table of Contents
1. Introduction
2. Preliminaries on the Borel reducibility hierarchy
3. Codings of separable Banach spaces and the local equivalence
4. The uniform homeomorphism on a class of Banach spaces
5. The complexity of the uniform homeomorphism and the local equivalence
6. Some special classes of separable Banach spaces
7. Nonisomorphic uniformly homeomorphic Banach spaces
References