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 withXA⊂XBwheneverA⊂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.
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