{"paper":{"title":"Variations on known and recent cardinality bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Fortunata Aurora Basile, Maddalena Bonanzinga, Nathan Carlson","submitted_at":"2017-09-29T17:05:34Z","abstract_excerpt":"Sapirovskii [18] proved that $|X|\\leq\\pi\\chi(X)^{c(X)\\psi(X)}$, for a regular space $X$. We introduce the $\\theta$-pseudocharacter of a Urysohn space $X$, denoted by $\\psi_\\theta (X)$, and prove that the previous inequality holds for Urysohn spaces replacing the bounds on celluarity $c(X)\\leq\\kappa$ and on pseudocharacter $\\psi(X)\\leq\\kappa$ with a bound on Urysohn cellularity $Uc(X)\\leq\\kappa$ (which is a weaker conditon because $Uc(X)\\leq c(X)$) and on $\\theta$-pseudocharacter $\\psi_\\theta (X)\\leq\\kappa$ respectivly (note that in general $\\psi(\\cdot)\\leq\\psi_\\theta (\\cdot)$ and in the class "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10497","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"}