{"paper":{"title":"Lower separation axioms via Borel and Baire algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Adam Barto\\v{s}, Taras Banakh","submitted_at":"2017-05-21T05:45:53Z","abstract_excerpt":"Let $\\kappa$ be an infinite regular cardinal. We define a topological space $X$ to be $T_{\\kappa-Borel}$-space (resp. a $T_{\\kappa-BP}$-space) if for every $x\\in X$ the singleton $\\{x\\}$ belongs to the smallest $\\kappa$-additive algebra of subsets of $X$ that contains all open sets (and all nowhere dense sets) in $X$. Each $T_1$-space is a $T_{\\kappa-Borel}$-space and each $T_{\\kappa-Borel}$-space is a $T_0$-space. On the other hand, $T_{\\kappa-BP}$-spaces need not be $T_0$-spaces.\n  We prove that a topological space $X$ is a $T_{\\kappa-Borel}$-space (resp. a $T_{\\kappa-BP}$-space) if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07399","kind":"arxiv","version":2},"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"}