{"paper":{"title":"Closure of rigid semianalytic sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hans Schoutens (Mathematical Institute, Oxford University)","submitted_at":"1997-06-21T00:00:00Z","abstract_excerpt":"Let K be an algebraically closed field of characteristic zero, endowed with a complete nonarchimedean norm. Let X be a K-rigid analytic variety and \\Sigma a semianalytic subset of X. Then the closure of \\Sigma in X with respect to the canonical topology is again semianalytic. The proof uses Embedded Resolution of Singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9706227","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"}