English

Baire theorem for ideals of sets

Functional Analysis 2016-03-30 v1

Abstract

We study ideals I\mathcal{I} on N\mathbb{N} satisfying the following Baire-type property: if XX is a complete metric space and {XA ⁣:AI}\{X_{A} \colon A \in \mathcal{I} \} is a family of nowhere dense subsets of XX with XAXBX_{A} \subset X_{B} whenever ABA \subset B, then AIXAX\bigcup_{A \in \mathcal{I}}{X_{A}} \neq 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 XX.

Keywords

Cite

@article{arxiv.1603.08699,
  title  = {Baire theorem for ideals of sets},
  author = {A. Avilés and V. Kadets and A. Pérez and S. Solecki},
  journal= {arXiv preprint arXiv:1603.08699},
  year   = {2016}
}

Comments

To appear in Journal of Mathematical Analysis and Applications

R2 v1 2026-06-22T13:20:21.766Z