{"paper":{"title":"Anti-Urysohn spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2015-09-04T11:57:23Z","abstract_excerpt":"All spaces are assumed to be infinite Hausdorff spaces. We call a space \"anti-Urysohn\" $($AU in short$)$ iff any two non-emty regular closed sets in it intersect. We prove that\n  $\\bullet$ for every infinite cardinal ${\\kappa}$ there is a space of size ${\\kappa}$ in which fewer than $cf({\\kappa})$ many non-empty regular closed sets always intersect;\n  $\\bullet$ there is a locally countable AU space of size $\\kappa$ iff $\\omega \\le \\kappa \\le 2^{\\mathfrak c}$.\n  A space with at least two non-isolated points is called \"strongly anti-Urysohn\" $($SAU in short$)$ iff any two infinite closed sets in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01420","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"}