Lángi, Zsolt and Naszódi, Márton (2017) On multiple Borsuk numbers in normed spaces. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 54 (1). pp. 13-26. ISSN 0081-6906
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Abstract
Hujter and L'angi defined the k-fold Borsuk number of a set S in Euclidean n-space of diameter d > 0 as the smallest cardinality of a family F of subsets of S, of diameters strictly less than d, such that every point of S belongs to at least k members of F. 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.
| Item Type: | Article |
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| Uncontrolled Keywords: | SETS; DIAMETER; Covering; CONSTANT WIDTH; multiple chromatic number; complete; bodies of constant width; unique completion; Borsuk's problem; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 22 Sep 2019 14:32 |
| Last Modified: | 22 Sep 2019 14:32 |
| URI: | http://real.mtak.hu/id/eprint/100307 |
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