On the complexity of the uniform homeomorphism relation between separable Banach spaces

Su Gao, Steve Jackson, Bünyamin Sarı
2011 Transactions of the American Mathematical Society  
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 complexity of the uniform homeomorphism.
doi:10.1090/s0002-9947-2011-05075-0 fatcat:iyqrjr6x3nanvnc54u27e2oipq