{"paper":{"title":"The non-Urysohn number of a topological space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ivan S. Gotchev","submitted_at":"2013-11-26T02:46:59Z","abstract_excerpt":"We call a nonempty subset $A$ of a topological space $X$ finitely non-Urysohn if for every nonempty finite subset $F$ of $A$ and every family $\\{U_x:x\\in F\\}$ of open neighborhoods $U_x$ of $x\\in F$, $\\cap\\{\\mathrm{cl}(U_x):x\\in F\\}\\ne\\emptyset$ and we define the non-Urysohn number of $X$ as follows: $nu(X):=1+\\sup\\{|A|:A$ is a finitely non-Urysohn subset of $X\\}$.\n  Then for any topological space $X$ and any subset $A$ of $X$ we prove the following inequalities: (1) $|\\mathrm{cl}_\\theta(A)|\\le |A|^{\\kappa(X)}\\cdot nu(X)$, (2) $|[A]_\\theta|\\le (|A|\\cdot nu(X))^{\\kappa(X)}$, (3) $|X|\\le nu(X)^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6544","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"}