Csikós, Balázs, Kiss, György, Swanepoel, Konrad and Oloff de Wet, P. (2009) Large antipodal families. Periodica Mathematica Hungarica, 58 (2). pp. 129-138. ISSN 0031-5303
Abstract
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.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.springer.com/math/journal/10998 |
| Additional Information: | © 2009 Springer |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Date Deposited: | 09 Oct 2009 09:46 |
| URL: | http://eprints.lse.ac.uk/25411/ |
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