The smooth ideal. Issue 1 (7th January 2016)

• Record Type: Journal Article
• Authors: Clemens, John D.; Conley, Clinton T.; Miller, Benjamin D.
• Is Part Of: Proceedings of the London Mathematical Society. Volume 112:Issue 1(2016:Jan.)
• Page Start: 57
• Page End: 80
• Publication Date: 2016-01-07
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdv069
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract : We give a classical proof of the generalization of the characterization of smoothness to quotients of Polish spaces by Borel equivalence relations. As an application, we describe the extent to which any given Borel equivalence relation on a Polish space is encoded by the correspondingσ ‐ideal generated by the family of Borel sets on which it is smooth.