On the complexity of the uniform homeomorphism relation

between separable Banach spaces

colorful horizontal rule

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

  

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This paper appeared in Transactions of the American Mathematical Society 363 (2011), no. 6, 3071-3099.

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