{"paper":{"title":"Generalizations of two cardinal inequalities of Hajnal and Juh\\'asz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ivan S. Gotchev","submitted_at":"2015-04-08T00:22:26Z","abstract_excerpt":"A non-empty subset $A$ of a topological space $X$ is called \\emph{finitely non-Hausdorff} if for every non-empty finite subset $F$ of $A$ and every family $\\{U_x:x\\in F\\}$ of open neighborhoods $U_x$ of $x\\in F$, $\\cap\\{U_x:x\\in F\\}\\ne\\emptyset$ and \\emph{the non-Hausdorff number $nh(X)$ of $X$} is defined as follows: $nh(X):=1+\\sup\\{|A|:A\\subset X$ is finitely non-Hausdorff$\\}$. Clearly, if $X$ is a Hausdorff space then $nh(X)=2$.\n  We define the \\emph{non-Urysohn number of $X$ with respect to the singletons}, $nu_s(X)$, as follows: $nu_s(X):=1+\\sup\\{\\mathrm{cl}_\\theta(\\{x\\}):x\\in X\\}$.\n  In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01790","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"}