Large antipodal families
Csikós, B., Kiss, G., Swanepoel, K.
& Oloff de Wet, P.
(2009).
Large antipodal families.
Periodica Mathematica Hungarica,
58(2), 129-138.
https://doi.org/10.1007/s10998-009-10129-9
& Oloff de Wet, P.
(2009).
Large antipodal families.
Periodica Mathematica Hungarica,
58(2), 129-138.
https://doi.org/10.1007/s10998-009-10129-9
A family {A i | i ∈ I} of sets in ℝ d is antipodal if for any distinct i, j ∈ I and any p ∈ A i , q ∈ A j , there is a linear functional ϕ:ℝ d → 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.