Baire theorem for ideals of sets

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1221-1231
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume445
Issue number2
DOIs
StatePublished - Jan 15 2017

Keywords

  • Analytic set
  • Baire theorem
  • Ideal of sets
  • Nowhere dense

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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