{"paper":{"title":"On non-separable families of positive homothetic convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Karoly Bezdek, Zsolt Langi","submitted_at":"2016-02-02T17:41:14Z","abstract_excerpt":"A finite family ${\\mathcal B}$ of balls with respect to an arbitrary norm in ${\\mathbb R}^d$ ($d\\geq 2$) is called a non-separable family if there is no hyperplane disjoint from $\\bigcup {\\mathcal B}$ that strictly separates some elements of ${\\mathcal B}$ from all the other elements of ${\\mathcal B}$ in ${\\mathbb R}^d$. In this paper we prove that if ${\\mathcal B}$ is a non-separable family of balls of radii $r_1, r_2,\\ldots , r_n$ ($n\\geq 2$) with respect to an arbitrary norm in ${\\mathbb R}^d$ ($d\\geq 2$), then $\\bigcup {\\mathcal B}$ can be covered by a ball of radius $\\sum_{i=1}^n r_i$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01020","kind":"arxiv","version":3},"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"}