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The complexity of the classification problem of continua


Authors: Cheng Chang and Su Gao
Journal: Proc. Amer. Math. Soc. 145 (2017), 1329-1342
MSC (2010): Primary 03E15, 54F15; Secondary 54H05, 46E15
DOI: https://doi.org/10.1090/proc/13288
Published electronically: November 18, 2016
MathSciNet review: 3589329
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Abstract: We prove that the homeomorphism problem for connected compact metric spaces is Borel bireducible with a universal orbit equivalence relation induced by a Borel action of a Polish group.


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Additional Information

Cheng Chang
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203
Email: chengchang@my.unt.edu

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

DOI: https://doi.org/10.1090/proc/13288
Keywords: Continuum, path-connected, compact metric space, Borel reducible, Borel bireducible, universal orbit equivalence relation
Received by editor(s): October 30, 2015
Received by editor(s) in revised form: April 2, 2016
Published electronically: November 18, 2016
Additional Notes: The second author acknowledges the US NSF grant DMS-1201290 for the support of his research.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society