{"paper":{"title":"Regular $G_\\delta$-diagonals and some upper bounds for cardinality of topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ivan S. Gotchev, Mikhail G. Tkachenko, Vladimir V. Tkachuk","submitted_at":"2015-06-15T16:51:22Z","abstract_excerpt":"We prove that, under CH, any space with a regular $G_\\delta$-diagonal and caliber $\\omega_1$ is separable; a corollary of this result answers, under CH, a question of Buzyakova. For any Urysohn space $X$, we establish the inequality $|X|\\le wL(X)^{s\\Delta_2(X)\\cdot{dot(X)}}$ which represents a generalization of a theorem of Basile, Bella, and Ridderbos. We also show that if $X$ is a Hausdorff space, then $|X|\\le(\\pi\\chi(X)\\cdot d(X))^{ot(X)\\cdot\\psi_c(X)}$; this result implies \\v{S}apirovski{\\u\\i}'s inequality $|X|\\le\\pi\\chi(X)^{c(X)\\cdot\\psi(X)}$ which only holds for regular spaces. It is als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04665","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"}