{"paper":{"title":"On the set of local extrema of a subanalytic function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jos\\'e F. Fernando","submitted_at":"2018-03-15T22:03:51Z","abstract_excerpt":"Let ${\\mathfrak F}$ be a category of subanalytic subsets of real analytic manifolds that is closed under basic set-theoretical and basic topological operations. Let $M$ be a real analytic manifold and denote ${\\mathfrak F}(M)$ the family of the subsets of $M$ that belong to ${\\mathfrak F}$. Let $f:X\\to{\\mathbb R}$ be a subanalytic function on a subset $X\\in{\\mathfrak F}(M)$ such that the inverse image under $f$ of each interval of ${\\mathbb R}$ belongs to ${\\mathfrak F}(M)$. Let ${\\rm Max}(f)$ be the set of local maxima of $f$ and consider ${\\rm Max}_\\lambda(f):={\\rm Max}(f)\\cap\\{f=\\lambda\\}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06017","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"}