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  • 1 Eötvös University Department of Geometry Budapest P.O.B. 120 Hungary H-1518
  • 2 University of Szeged Bolyai Institute Szeged Aradi vértanúk tere 1 Hungary H-6720
  • 3 Technische Universität Chemnitz Fakultät für Mathematik Chemnitz 09107 Germany
  • 4 University of South Africa Department of Decision Science PO Box 392 UNISA 0003 Pretoria South Africa
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Abstract  

A family {Ai | iI} of sets in ℝd is antipodal if for any distinct i, jI and any pAi, qAj, there is a linear functional ϕ:ℝd → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪iIAi. We study the existence of antipodal families of large finite or infinite sets in ℝ3.

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