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Midpoint sets contained in the unit sphere of a normed space

Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2011) Midpoint sets contained in the unit sphere of a normed space. Studia Scientiarum Mathematicarum Hungarica, 48 (2). pp. 180-192. ISSN 0081-6906

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Identification Number: 10.1556/SScMath.48.2011.2.1165


The midpoint set M(S) of a set S of points is the set of all midpoints of pairs of points in S. We study the largest cardinality of a midpoint set M(S) in a finite-dimensional normed space, such that M(S) is contained in the unit sphere, and S is outside the closed unit ball. We show in three dimensions that this maximum (if it exists) is determined by the facial structure of the unit ball. In higher dimensions no such relationship exists. We also determine the maximum for euclidean and sup norm spaces.

Item Type: Article
Official URL:
Additional Information: © 2011 Akadémiai Kiadó
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 Jun 2011 12:47
Last Modified: 16 May 2024 01:15

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