{"paper":{"title":"Domains of existence for finely holomorphic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alan Groot, Bent Fuglede, Jan Wiegerinck","submitted_at":"2017-06-08T09:57:20Z","abstract_excerpt":"We show that fine domains in $\\mathbf{C}$ with the property that they are Euclidean $F_\\sigma$ and $G_\\delta$, are in fact fine domains of existence for finely holomorphic functions. Moreover \\emph{regular} fine domains are also fine domains of existence. Next we show that fine domains such as $\\mathbf{C}\\setminus \\mathbf{Q}$ or $\\mathbf{C}\\setminus (\\mathbf{Q}\\times i\\mathbf{Q})$, more specifically fine domains $V$ with the properties that their complement contains a non-empty polar set $E$ that is of the first Baire category in its Euclidean closure $K$ and that $(K\\setminus E)\\subset V$, ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02498","kind":"arxiv","version":3},"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"}