{"paper":{"title":"Cardinality bounds involving the skew-$\\lambda$ Lindel\\\"of degree and its variants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jack Porter, Nathan Carlson","submitted_at":"2015-07-23T21:07:24Z","abstract_excerpt":"We introduce a modified closing-off argument that results in several improved bounds for the cardinalities of Hausdorff and Urysohn spaces. These bounds involve the cardinal invariant $skL(X,\\lambda)$, the skew-$\\lambda$ Lindel\\\"of degree of a space $X$, where $\\lambda$ is a cardinal. $skL(X,\\lambda)$ is a weakening of the Lindel\\\"of degree and is defined as the least cardinal $\\kappa$ such that if $\\mathcal{U}$ is an open cover of $X$ then there exists $\\mathcal{V}\\in [\\mathcal{U}]^{\\leq\\kappa}$ such that $|X\\backslash\\cup\\mathcal{V}|<\\lambda$. We show that if $X$ is Hausdorff then $|X|\\leq 2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06684","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"}