{"paper":{"title":"On Gibson functions with connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2014-07-24T10:17:49Z","abstract_excerpt":"A function $f:X\\to Y$ between topological spaces is said to be a {\\it weakly Gibson function} if $f(\\overline{G})\\subseteq \\overline{f(G)}$ for any open connected set \\mbox{$G\\subseteq X$}. We call a function $f:X\\to Y$ {\\it segmentary connected} if $X$ is topological vector space and $f([a,b])$ is connected for every segment $[a,b]\\subseteq X$. We show that if $X$ is a hereditarily Baire space, $Y$ is a metric space, \\mbox{$f:X\\to Y$} is a Baire-one function and one of the following conditions holds: (i) $X$ is a connected and locally connected space and $f$ is a weakly Gibson function, (ii) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6515","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"}