On multiple Borsuk numbers in normed spaces

Lángi, Zsolt and Naszódi, Márton (2015) On multiple Borsuk numbers in normed spaces. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA. ISSN 0081-6906 (Submitted)

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Abstract

Hujter and Lángi 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 �nite 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.

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