{"paper":{"title":"Weakly linearly Lindel\\\"of monotonically normal spaces are Lindel\\\"of","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"I. Juh\\'asz, R. G. Wilson, V. V. Tkachuk","submitted_at":"2016-10-14T15:40:40Z","abstract_excerpt":"We call a space $X$ {\\it weakly linearly Lindel\\\"of} if for any family $\\mathcal{U}$ of non-empty open subsets of $X$ of regular uncountable cardinality $\\kappa$, there exists a point $x\\in X$ such that every neighborhood of $x$ meets $\\kappa$-many elements of $\\mathcal{U}$. We also introduce the concept of {\\it almost discretely Lindel\\\"of} spaces as the ones in which every discrete subspace can be covered by a Lindel\\\"of subspace. We prove that, in addition to linearly Lindel\\\"of spaces, both weakly Lindel\\\"of spaces and almost discretely Lindel\\\"of spaces are weakly linearly Lindel\\\"of.\n  T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04506","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"}