{"paper":{"title":"Klee-Phelps Convex Groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"J.F. Peters, M. A. \\\"Ozt\\\"urk, M. U\\c{c}kun","submitted_at":"2014-11-04T15:02:43Z","abstract_excerpt":"We prove that a pair of proximal Klee-Phelps convex groupoids $A(\\circ)$,$B(\\circ)$ in a finite-dimensional normed linear space $E$ are normed proximal, {\\em i.e.}, $A(\\circ)\\ \\delta\\ B(\\circ)$ if and only if the groupoids are normed proximal. In addition, we prove that the groupoid neighbourhood $N_z(\\circ)\\subseteq S_z(\\circ)$ is convex in $E$ if and only if $N_z(\\circ) = S_z(\\circ)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0934","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"}