{"paper":{"title":"The weight and Lindel\\\"of property in spaces and topological groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Mikhail G. Tkachenko","submitted_at":"2015-09-09T18:00:33Z","abstract_excerpt":"We show that if $Y$ is a dense subspace of a Tychonoff space $X$, then $w(X)\\leq nw(Y)^{Nag(Y)}$, where $Nag(Y)$ is the Nagami number of $Y$. In particular, if $Y$ is a Lindel\\\"of $\\Sigma$-space, then $w(X)\\leq nw(Y)^\\omega\\leq nw(X)^\\omega$.\n  Better upper bounds for the weight of topological groups are given. For example, if a topological group $H$ contains a dense subgroup $G$ such that $G$ is a Lindel\\\"of $\\Sigma$-space, then $w(H)=w(G)\\leq \\psi(G)^\\omega$. Further, if a Lindel\\\"of $\\Sigma$-space $X$ generates a dense subgroup of a topological group $H$, then $w(H)\\leq 2^{\\psi(X)}$.\n  Seve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02874","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"}