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

Library availability

Discover UIUC Full Text

Cite this

@article{aa79cee3304e4d68bbad4860dba8538d,

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 = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

month = jan,

day = "15",

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

language = "English (US)",

volume = "445",

pages = "1221--1231",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Baire theorem for ideals of sets

AU - Avilés, A.

AU - Kadets, V.

AU - Pérez, A.

AU - Solecki, S.

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

UR - http://www.scopus.com/inward/record.url?scp=84960172854&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960172854&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.02.075

DO - 10.1016/j.jmaa.2016.02.075

M3 - Article

AN - SCOPUS:84960172854

SN - 0022-247X

VL - 445

SP - 1221

EP - 1231

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Baire theorem for ideals of sets

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this