{"paper":{"title":"On multiple Borsuk numbers in normed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"M\\'arton Nasz\\'odi, Zsolt L\\'angi","submitted_at":"2013-11-13T16:25:56Z","abstract_excerpt":"Hujter and L\\'angi introduced the $k$-fold Borsuk number of a set $S$ in Euclidean $n$-space of diameter $d > 0$ as the smallest cardinality of a family $\\mathcal F$ of subsets of $S$, of diameters strictly less than $d$, such that every point of $S$ belongs to at least $k$ members of $\\mathcal F$.\n  We investigate whether a $k$-fold Borsuk covering of a set $S$ in a finite dimensional real normed space can be extended to a completion of $S$. Furthermore, we determine the $k$-fold Borsuk number of sets in not angled normed planes, and give a partial characterization for sets in angled planes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3193","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"}