{"paper":{"title":"Cardinalities of weakly Lindel\\\"of spaces with regular $G_\\kappa$-diagonals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ivan S. Gotchev","submitted_at":"2015-04-08T00:03:43Z","abstract_excerpt":"For a Urysohn space $X$ we define the regular diagonal degree $\\overline{\\Delta}(X)$ of $X$ to be the minimal infinite cardinal $\\kappa$ such that $X$ has a regular $G_\\kappa$-diagonal i.e. there is a family $(U_\\eta:\\eta<\\kappa)$ of open neighborhoods of $\\Delta_X=\\{(x,x)\\in X^2:x\\in X\\}$ in $X^2$ such that $\\Delta_X = \\bigcap_{\\eta<\\kappa} \\overline{U}_\\eta$.\n  In this paper we show that if $X$ is a Urysohn space then: (1) $|X|\\leq 2^{c(X)\\cdot\\overline{\\Delta}(X)}$; (2) $|X|\\leq 2^{\\overline{\\Delta}(X)\\cdot 2^{wL(X)}}$; (3) $|X|\\le wL(X)^{\\overline{\\Delta}(X)\\cdot\\chi(X)}$; and (4) $|X|\\le "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01785","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"}