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Large antipodal families

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Abstract

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

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Authors and Affiliations

  1. Department of Geometry, Eötvös University, Budapest, P.O.B. 120, Hungary, H-1518

    Balázs Csikós & György Kiss

  2. Bolyai Institute, University of Szeged, Szeged, Aradi vértanúk tere 1, Hungary, H-6720

    György Kiss

  3. Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, 09107, Germany

    Konrad J. Swanepoel

  4. Department of Decision Science, University of South Africa, PO Box 392, UNISA 0003, Pretoria, South Africa

    P. Oloff de Wet

Authors
  1. Balázs Csikós
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  2. György Kiss
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  3. Konrad J. Swanepoel
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  4. P. Oloff de Wet
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Corresponding author

Correspondence to Balázs Csikós.

Additional information

Communicated by Mária B. Szendrei

Dedicated to Ted Bisztriczky on the occasion of his 60th birthday

The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.

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Csikós, B., Kiss, G., Swanepoel, K.J. et al. Large antipodal families. Period Math Hung 58, 129–138 (2009). https://doi.org/10.1007/s10998-009-10129-9

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  • DOI: https://doi.org/10.1007/s10998-009-10129-9

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