{"paper":{"title":"Severi-Bouligand tangents, Frenet frames and Riesz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Daniele Mundici, Leonardo Manuel Cabrer","submitted_at":"2013-08-03T06:10:49Z","abstract_excerpt":"It was recently proved that a compact set $X\\subseteq \\mathbb R^2$ has an outgoing Severi-Bouligand tangent vector $u\\not=0$ at $x\\in X$ iff some principal ideal of the Riesz space $\\mathcal R(X)$ of piecewise linear functions on $X$ is not an intersection of maximal ideals. \"Outgoing\" means $X\\cap [x,x+u]=\\{x\\}$.\n  Suppose now $X\\subseteq \\mathbb{R}^n$ and some principal ideal of $\\mathcal R(X)$ is not an intersection of maximal ideals. We prove that this is equivalent to saying that $X$ contains a sequence $\\{x_i\\}$ whose Frenet $k$-frame $(u_1,\\ldots,u_k)$ is an outgoing Severi-Bouligand ta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0662","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"}