{"paper":{"title":"On weakly Gibson $F_\\sigma$-measurable mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2014-07-24T10:21:06Z","abstract_excerpt":"A function $f:X\\to Y$ between topological spaces is said to be a {\\it weakly Gibson function} if $f(\\overline{U})\\subseteq \\overline{f(U)}$ for any open connected set \\mbox{$U\\subseteq X$}. We prove that if $X$ is a locally connected hereditarily Baire space and $Y$ is a $T_1$-space then an $F_\\sigma$-measurable mapping $f:X\\to Y$ is weakly Gibson if and only if for any connected set $C\\subseteq X$ with the dense connected interior\n  the image $f(C)$ is connected. Moreover, we show that each weakly Gibson $F_\\sigma$-measurable mapping $f:\\mathbb R^n\\to Y$, where $Y$ is a $T_1$-space, has a con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6517","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"}