{"paper":{"title":"Cardinal inequalities for $S(n)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ivan S. Gotchev","submitted_at":"2018-10-30T20:44:46Z","abstract_excerpt":"Hajnal and Juh\\'asz proved that if $X$ is a $T_1$-space, then $|X|\\le 2^{s(X)\\psi(X)}$, and if $X$ is a Hausdorff space, then $|X|\\le 2^{c(X)\\chi(X)}$ and $|X|\\le 2^{2^{s(X)}}$. Schr\\\"oder sharpened the first two estimations by showing that if $X$ is a Hausdorff space, then $|X|\\le 2^{Us(X)\\psi_c(X)}$, and if $X$ is a Urysohn space, then $|X|\\le 2^{Uc(X)\\chi(X)}$.\n  In this paper, for any positive integer $n$ and some topological spaces $X$, we define the cardinal functions $\\chi_n(X)$, $\\psi_n(X)$, $s_n(X)$, and $c_n(X)$, called respectively $S(n)$-character, $S(n)$-pseudocharacter, $S(n)$-sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12998","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"}