{"paper":{"title":"Exponential laws for spaces of differentiable functions on topological groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Natalie Nikitin","submitted_at":"2016-08-22T09:25:06Z","abstract_excerpt":"Smooth functions $f:G\\to E$ from a topological group $G$ to a locally convex space $E$ were considered by Riss (1953), Boseck, Czichowski and Rudolph (1981), Belti\\c{t}\\u{a} and Nicolae (2015), and others, in varying degrees of generality. The space $C^\\infty(G,E)$ of such functions carries a natural topology, the compact-open $C^\\infty$-topology. For topological groups $G$ and $H$, we show that $C^\\infty(G\\times H,E)\\cong C^\\infty(G,C^\\infty(H,E))$ as a locally convex space, whenever both $G$ and $H$ are metrizable or both $G$ and $H$ are locally compact. Likewise, $C^k(G, C^l(H,E))$ can be i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06095","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"}