{"paper":{"title":"On the cardinality of the $\\theta$-closed hull of sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Andrei Catalioto, Boaz Tsaban, Bruno Antonio Pansera, Filippo Cammaroto","submitted_at":"2012-03-26T21:38:30Z","abstract_excerpt":"The \\theta-closed hull of a set A in a topological space is the smallest set C containing A such that, whenever all $closed$ neighborhoods of a point intersect C, this point is in C.\n  We define a new topological cardinal invariant function, the $\\theta-bitighness small number$ of a space X, bts_theta(X), and prove that in every topological space X, the cardinality of the theta-closed hull of each set A is at most |A|^{bts_theta(X)}. Using this result, we synthesize all earlier results on bounds on the cardinality of theta-closed hulls.\n  We provide applications to P-spaces and to the almost-L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5824","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"}