{"paper":{"title":"Baire theorem for ideals of sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Avil\\'es, A. P\\'erez, S. Solecki, V. Kadets","submitted_at":"2016-03-29T09:57:31Z","abstract_excerpt":"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 $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08699","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}