{"paper":{"title":"Diagonals of separately continuous functions and their analogs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Oleksandr Sobchuk, Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2014-07-22T06:12:19Z","abstract_excerpt":"We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\\to Z$ there exists a separately continuous mapping $f:X^2\\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\\in X$. Under a mild assumptions on $X$ and $Z$ we obtain that diagonals of separately continuous mappings $f:X^2\\to Z$ are exactly Baire-one functions, and diagonals of mappings $f:X^2\\to Z$ which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5745","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"}