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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.01420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-04T11:57:23Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"9efb0a9aaf0a98383aaed472807366d1aba31668908e9d8c54e6e172d35a0684","abstract_canon_sha256":"f46997fe76fab861c0d2aef31e9adabc5bf80e16a37d3e3bbf15409ad8312023"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:57.712091Z","signature_b64":"ocvSwNUl9mZujOk3KS5x5VtgTy68HaIyT7mwrw4CxzDE1SM8hlA0uwaLEY3XTPYRSxlGYcA7FDyrZJuYgMStBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"680e781b4674cf2477c8969ea2e0fa4a1f607b149ccaca28e115894900168753","last_reissued_at":"2026-05-18T01:33:57.711734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:57.711734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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