{"paper":{"title":"Cardinal functions $F_{\\theta}(X)$ and $t_{\\theta}(X)$ for H-closed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Andrei Catalioto, Filippo Cammaroto, Jack Porter","submitted_at":"2012-06-28T03:22:45Z","abstract_excerpt":"In this article, starting with results from a paper by Cammaroto and Ko\\v{c}inac in 1993, we prove that $t_{\\theta}(X) = t_{\\theta}(X_{s}) = t(X_{s}) = F_{\\theta}(X) = F_{\\theta}(X_{s}) = F(X_{s})$ for every H-closed and Urysohn space and we present some useful examples to study the full relationships among the cardinal functions $t$, $t_{\\theta}$, $F$ and $F_{\\theta}$ in the context of H-closed and Urysohn spaces. Also, we construct an H-closed space $H$ for which $F_{\\theta}(H) < t_{\\theta}(H)$. Two questions posed by Cammaroto and Ko\\v{c}inac about H-closed spaces are answered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6555","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"}