{"paper":{"title":"$G_\\delta$ covers of compact spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Paul Szeptycki, Santi Spadaro","submitted_at":"2016-05-18T15:51:36Z","abstract_excerpt":"We solve a long standing question due to Arhangel'skii by constructing a compact space which has a $G_\\delta$ cover with no continuum-sized ($G_\\delta$)-dense subcollection. We also prove that in a countably compact weakly Lindel\\\"of normal space of countable tightness, every $G_\\delta$ cover has a $\\mathfrak{c}$-sized subcollection with a $G_\\delta$-dense union and that in a Lindel\\\"of space with a base of multiplicity continuum, every $G_\\delta$ cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De La Ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05630","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"}