{"paper":{"title":"Homomorphisms into totally disconnected, locally compact groups with dense image","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Colin D. Reid, Phillip R. Wesolek","submitted_at":"2015-09-01T06:34:42Z","abstract_excerpt":"Let $\\phi: G \\rightarrow H$ be a group homomorphism such that $H$ is a totally disconnected locally compact (t.d.l.c.) group and the image of $\\phi$ is dense. We show that all such homomorphisms arise as completions of $G$ with respect to uniformities of a particular kind. Moreover, $H$ is determined up to a compact normal subgroup by the pair $(G,\\phi^{-1}(L))$, where $L$ is a compact open subgroup of $H$. These results generalize the well-known properties of profinite completions to the locally compact setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00156","kind":"arxiv","version":2},"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"}