The Smooth Ideal

John D. Clemens; Clinton T. Conley; Benjamin D. Miller

doi:10.1112/plms/pdv069

The Smooth Ideal

John D. Clemens
, Clinton T. Conley
, Benjamin D. Miller

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 corresponding σ -ideal generated by the family of Borel sets on which it is smooth.

Original language	American English
Journal	Proceedings of the London Mathematical Society
Volume	112
Issue number	1
DOIs	https://doi.org/10.1112/plms/pdv069
State	Published - Jan 2016
Externally published	Yes

EGS Disciplines

Mathematics

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title = "The Smooth Ideal",

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 corresponding σ -ideal generated by the family of Borel sets on which it is smooth. ",

author = "Clemens, \{John D.\} and Conley, \{Clinton T.\} and Miller, \{Benjamin D.\}",

note = "Mathematics Department, Southern Illinois University,, Neckers, Carbondale,, IL, USA Search for more papers by this author Department of Mathematics, Carnegie Mellon University, Pittsburgh,, PA, USA Search for more papers by this author Corresponding author Kurt G{\"o}del Research Center for Mathematical Logic, Universit{\"a}t Wien, Wien, Austria Search for more papers by this author 2010 Mathematics Subject Classification 03E15 (primary), 28A05 (secondary).",

year = "2016",

month = jan,

doi = "10.1112/plms/pdv069",

language = "American English",

volume = "112",

number = "1",

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T1 - The Smooth Ideal

AU - Clemens, John D.

AU - Conley, Clinton T.

AU - Miller, Benjamin D.

N1 - Mathematics Department, Southern Illinois University,, Neckers, Carbondale,, IL, USA Search for more papers by this author Department of Mathematics, Carnegie Mellon University, Pittsburgh,, PA, USA Search for more papers by this author Corresponding author Kurt Gödel Research Center for Mathematical Logic, Universität Wien, Wien, Austria Search for more papers by this author 2010 Mathematics Subject Classification 03E15 (primary), 28A05 (secondary).

PY - 2016/1

Y1 - 2016/1

N2 - 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 corresponding σ -ideal generated by the family of Borel sets on which it is smooth.

AB - 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 corresponding σ -ideal generated by the family of Borel sets on which it is smooth.

UR - http://dx.doi.org/10.1112/plms/pdv069

U2 - 10.1112/plms/pdv069

DO - 10.1112/plms/pdv069

M3 - Article

VL - 112

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 1

ER -

The Smooth Ideal

Abstract

EGS Disciplines

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