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


Authors: Su Gao, Steve Jackson and Bünyamin Sarı
Journal: Trans. Amer. Math. Soc. 363 (2011), 3071-3099
MSC (2010): Primary 46B80, 54H05; Secondary 46B07, 03E75
DOI: https://doi.org/10.1090/S0002-9947-2011-05075-0
Published electronically: January 27, 2011
MathSciNet review: 2775799
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Abstract: 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.


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Additional Information

Su Gao
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203-5017
Email: sgao@unt.edu

Steve Jackson
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203-5017
Email: jackson@unt.edu

Bünyamin Sarı
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203-5017
Email: bunyamin@unt.edu

DOI: https://doi.org/10.1090/S0002-9947-2011-05075-0
Keywords: Uniform homeomorphism, Borel reducibility, analytic equivalence relations, local equivalence
Received by editor(s): January 27, 2009
Received by editor(s) in revised form: April 10, 2009
Published electronically: January 27, 2011
Additional Notes: The first author acknowledges the partial support of the NSF grant DMS-0501039 and a Templeton Foundation research grant for his research.
The third author acknowledges an NSF funded Young Investigator Award of the Analysis and Probability workshop at the Texas A&M University in 2008.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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