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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.01790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-04-08T00:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"2594e0f0a7f90856ad9c77f83ae21644c40184540729b2b7d0fdba7d64a52bd4","abstract_canon_sha256":"3200451054981723aa1fec4ee35449c2ef4868d966ade6afd6b3452051f8fc83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:18.364007Z","signature_b64":"INKuFoN4z02CnyRzWDKonE9JFXxS5H6p8KAXA7eXntvu8aijK5MD6MA3aoPQ8RVsNIyKvI6uOzyKN5RvfZ4gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76d8f5b68070d230567994d1fdc0c0ab719553c4f2fc65a516f9d9e2c2e31ea0","last_reissued_at":"2026-05-18T02:19:18.363430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:18.363430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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$\\}$. 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