{"paper":{"title":"New results about Q and $\\Delta$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"\\'Akos Sz\\'ekely, J\\'anos Bal\\'azs Ivanyos","submitted_at":"2026-07-01T15:29:30Z","abstract_excerpt":"A topological space \\(X\\) is called a \\(Q\\)-space if every subset of \\(X\\) is a \\(G_\\delta\\)-set, and \\(X\\) is a \\(\\Delta\\)-space if for any decreasing sequence \\(\\{D_n : n \\in\\omega\\}\\) of subsets of \\(X\\) with empty intersection there is a decreasing sequence \\(\\{U_n : n \\in \\omega\\}\\) of open sets with empty intersection such that \\(D_n \\subseteq U_n\\) for all \\(n \\in\\omega\\).\n  Our main result shows that the following statements are equiconsistent:\n  (1) There exists a measurable cardinal;\n  (2) There exists a crowded Baire \\(T_1\\) \\(\\Delta\\)-space;\n  (3) There exists a crowded Baire \\(T_4"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01068","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01068/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}