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arXiv · 1603.08699

Baire theorem for ideals of sets

A. Avilés·V. Kadets·A. Pérez·S. Solecki
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Abstract

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

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A. Avilés, V. Kadets, A. Pérez, S. Solecki. 2016-03-29. Baire theorem for ideals of sets. https://doi.org/10.1016/j.jmaa.2016.02.075

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