{"paper":{"title":"On Some Idempotent and Non-Associative Convex Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Walter Briec","submitted_at":"2013-11-04T13:17:34Z","abstract_excerpt":"$\\mathbb B$-convexity was defined in [7] as a suitable Kuratowski-Painlev\\'e upper limit of linear convexities over a finite dimensional Euclidean vector space. Excepted in the special case where convex sets are subsets of $\\mathbb R^n_ +$, $\\mathbb B$-convexity was not defined with respect to a given explicit algebraic structure. This is done in that paper, which proposes an extension of $\\mathbb B$-convexity to the whole Euclidean vector space. An unital idempotent and non-associative magma is defined over the real set and an extended $n$-ary operation is introduced. Along this line, the exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0690","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"}