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Large antipodal families

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

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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
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Oct 2009 09:46
URL: http://eprints.lse.ac.uk/25411/

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