{"paper":{"title":"On the cardinality of Hausdorff spaces and H-closed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jack Porter, Nathan Carlson","submitted_at":"2016-10-28T14:46:34Z","abstract_excerpt":"We introduce the cardinal invariant $aL^\\prime(X)$ and show that $|X|\\leq 2^{aL^\\prime(X)\\chi(X)}$ for any Hausdorff space $X$ (a corollary of Theorem 4.4. This invariant has the properties a) $aL^\\prime(X)=\\aleph_0$ if $X$ is H-closed, and b) $aL(X)\\leq aL^\\prime(X)\\leq aL_c(X)$. Theorem 4.4 then gives a new improvement of the well-known Hausdorff bound $2^{L(X)\\chi(X)}$ from which it follows that $|X|\\leq 2^{\\psi_c(X)}$ if $X$ is H-closed (Dow/Porter [5]). The invariant $aL^\\prime(X)$ is constructed using convergent open ultrafilters and an operator $c:\\scr{P}(X)\\to\\scr{P}(X)$ with the prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09245","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"}