Large antipodal families

Balázs Csikós; György Kiss; Konrad Swanepoel; P. Oloff de Wet

doi:10.1007/s10998-009-10129-9

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 58: Issue 2

Large antipodal families

Authors:

Balázs Csikós

Balázs Csikós Eötvös University Department of Geometry Budapest P.O.B. 120 Hungary H-1518

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György Kiss

György Kiss

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Konrad Swanepoel

Konrad Swanepoel Technische Universität Chemnitz Fakultät für Mathematik Chemnitz 09107 Germany

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P. Oloff de Wet

P. Oloff de Wet University of South Africa Department of Decision Science PO Box 392 UNISA 0003 Pretoria South Africa

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Pages:: 129–138

Online Publication Date:: 31 May 2009

Publication Date:: 01 Jun 2009

Article Category:: Research Article

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

Keywords:: 52C35; antipodal set; strictly antipodal set; antipodal family of sets; strictly antipodal family of sets

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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∈IA_i. We study the existence of antipodal families of large finite or infinite sets in ℝ³.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)