{"paper":{"title":"On the resolvability of Lindel\\\"of-generated and (countable extent)-generated spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2018-04-09T14:24:38Z","abstract_excerpt":"Given a topological property $P$, we say that the space $X$ is $P$-generated if for any subset $A\\subset X$ that is not open in $X$ there is a subspace $Y \\subset X$ with property $P$ such that $A\\cap Y$ is not open in $Y$. (Of course, in this definition we could replace \"open\" with \"closed\".)\n  In this paper we prove the following two results:\n  (1) Every Lindel\\\"of-generated regular space $X$ satisfying $|X|=\\Delta(X)={\\omega}_1$ is ${\\omega}_1$-resolvable.\n  (2) Any (countable extent)-generated regular space $X$ satisfying $\\Delta(X)>{\\omega}$ is ${\\omega}$-resolvable.\n  These are significa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03019","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"}