{"paper":{"title":"On cardinality bounds involving the weak Lindel\\\"of degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angelo Bella, Nathan Carlson","submitted_at":"2016-10-27T20:06:43Z","abstract_excerpt":"We give a general closing-off argument in Theorem 2.1 from which several corollaries follow, including (1) if $X$ is a locally compact Hausdorff space then $|X|\\leq 2^{wL(X)\\psi(X)}$, and (2) if $X$ is a locally compact power homogeneous Hausdorff space then $|X|\\leq 2^{wL(X)t(X)}$. The first extends the well-known cardinality bound $2^{\\psi(X)}$ for a compactum $X$ in a new direction. As $|X|\\leq 2^{wL(X)\\chi(X)}$ for a normal space $X$ [3], this enlarges the class of known Tychonoff spaces for which this bound holds. In 2.10 we give a short, direct proof of (1) that does not use 2.1. Yet 2.1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08996","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"}