Baire theorem for ideals of sets

A. Avilés; V. Kadets; A. Pérez; S. Solecki

doi:10.1016/j.jmaa.2016.02.075

Baire theorem for ideals of sets

A. Avilés
, V. Kadets
, A. Pérez
, S. Solecki

Mathematics

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

Abstract

We study ideals I on N satisfying the following Baire-type property: if X is a complete metric space and {X_A:A∈I} is a family of nowhere dense subsets of X with X_A⊂X_B whenever A⊂B, then ⋃_A∈IX_A≠X. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of X.

Original language	English (US)
Pages (from-to)	1221-1231
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	445
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.02.075
State	Published - Jan 15 2017

Keywords

Analytic set
Baire theorem
Ideal of sets
Nowhere dense

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2016.02.075

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title = "Baire theorem for ideals of sets",

abstract = "We study ideals I on N satisfying the following Baire-type property: if X is a complete metric space and \{XA:A∈I\} is a family of nowhere dense subsets of X with XA⊂XB whenever A⊂B, then ⋃A∈IXA≠X. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of X.",

keywords = "Analytic set, Baire theorem, Ideal of sets, Nowhere dense",

author = "A. Avil{\'e}s and V. Kadets and A. P{\'e}rez and S. Solecki",

note = "The first author was supported by MINECO and FEDER ( MTM2014-54182-P ) and by Fundaci\textbackslash{}u00F3n S\textbackslash{}u00E9neca \textbackslash{}u2013 Regi\textbackslash{}u00F3n de Murcia ( 19275/PI/14 ). The research of the second author partially was done during his stay in Murcia under the support of MINECO and FEDER projects MTM2008-05396 and MTM2011-25377 . The third author was partially supported by the MINECO/FEDER project MTM2014-57838-C2-1-P and a PhD fellowship of \textbackslash{}u201C La Caixa Foundation \textbackslash{}u201D. The fourth author was supported by NSF grant DMS-1266189 .",

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doi = "10.1016/j.jmaa.2016.02.075",

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T1 - Baire theorem for ideals of sets

AU - Avilés, A.

AU - Kadets, V.

AU - Pérez, A.

AU - Solecki, S.

N1 - The first author was supported by MINECO and FEDER ( MTM2014-54182-P ) and by Fundaci\u00F3n S\u00E9neca \u2013 Regi\u00F3n de Murcia ( 19275/PI/14 ). The research of the second author partially was done during his stay in Murcia under the support of MINECO and FEDER projects MTM2008-05396 and MTM2011-25377 . The third author was partially supported by the MINECO/FEDER project MTM2014-57838-C2-1-P and a PhD fellowship of \u201C La Caixa Foundation \u201D. The fourth author was supported by NSF grant DMS-1266189 .

PY - 2017/1/15

Y1 - 2017/1/15

N2 - We study ideals I on N satisfying the following Baire-type property: if X is a complete metric space and {XA:A∈I} is a family of nowhere dense subsets of X with XA⊂XB whenever A⊂B, then ⋃A∈IXA≠X. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of X.

AB - We study ideals I on N satisfying the following Baire-type property: if X is a complete metric space and {XA:A∈I} is a family of nowhere dense subsets of X with XA⊂XB whenever A⊂B, then ⋃A∈IXA≠X. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of X.

KW - Analytic set

KW - Baire theorem

KW - Ideal of sets

KW - Nowhere dense

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DO - 10.1016/j.jmaa.2016.02.075

M3 - Article

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JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Baire theorem for ideals of sets

Abstract

Keywords

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