{"paper":{"title":"The weights of closed subgroups of a locally compact group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Karl H. Hofmann, Salvador Hern\\'andez, Sidney A. Morris","submitted_at":"2012-01-18T15:08:38Z","abstract_excerpt":"Let $G$ be an infinite locally compact group and $\\aleph$ a cardinal satisfying $\\aleph_0\\le\\aleph\\le w(G)$ for the weight $w(G)$ of $G$. It is shown that there is a closed subgroup $N$ of $G$ with $w(N)=\\aleph$. Sample consequences are:\n  (1) Every infinite compact group contains an infinite closed metric subgroup.\n  (2) For a locally compact group $G$ and $\\aleph$ a cardinal satisfying $\\aleph_0\\le\\aleph\\le \\lw(G)$, where $\\lw(G)$ is the local weight of $G$, there are either no infinite compact subgroups at all or there is a compact subgroup $N$ of $G$ with $w(N)=\\aleph$.\n  (3) For an infini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3814","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"}