On the complexity of the uniform homeomorphism
relation
between separable Banach spaces
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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
This
paper appeared in Transactions of the American
Mathematical Society
363 (2011), no. 6, 3071-3099.