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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.6517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-07-24T10:21:06Z","cross_cats_sorted":[],"title_canon_sha256":"0533b1aa06991dbacab3527a040f899ea85da66f51dace62c6fec20efe35931f","abstract_canon_sha256":"d43dee109d1fe494daa5b32e58f0610f558aa21eeb71ea846b0952b487d4428b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:38.563402Z","signature_b64":"bgVPOHWbn8iv9XzuhbRfjuIGZtFn0nFxnClyw+Q/NTrYDWoqP5HcP3HOg8N9gs8Izdhvep6LGli4PnwBj3QvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faf5bab73d0c11755f6f856834a0812a9448cc7e01a025bfa0ac0457c47ef63e","last_reissued_at":"2026-05-18T02:46:38.562923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:38.562923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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