{"paper":{"title":"Grauert's theorem for subanalytic open sets in real analytic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Daniel Barlet, Teresa Monteiro Fernandes","submitted_at":"2010-11-18T15:12:09Z","abstract_excerpt":"By open neighbourhood of an open subset $\\Omega$ of $\\mathbb{R}^n$ we mean an open subset $\\Omega'$ of $\\mathbb{C}^n$ such that $\\mathbb{R}^n\\cap\\Omega'=\\Omega.$ A well known result of H. Grauert implies that any open subset of $\\mathbb{R}^n$ admits a fundamental system of Stein open neighbourhoods in $\\mathbb{C}^n$. Another way to state this property is to say that each open subset of $\\mathbb{R}^n$ is Stein. We shall prove a similar result in the subanalytic category, so, under the assumption that $\\Omega$ is a subanalytic relatively compact open subset in a real analytic manifold, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4208","kind":"arxiv","version":2},"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"}