Notes About the Caratheodory Number

被引：14

作者：

Barany, Imre ^{[2
,3
]}

Karasev, Roman ^{[1
,4
]}

机构：

[1] Moscow Inst Phys & Technol, Dept Math, Dolgoprudnyi 141700, Russia

[2] Hungarian Acad Sci, Renyi Inst Math, H-1364 Budapest, Hungary

[3] UCL, Dept Math, London WC1E 6BT, England

[4] Yaroslavl State Univ, Lab Discrete & Computat Geometry, Yaroslavl 150000, Russia

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2012年 / 48卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Caratheodory's theorem; Helly's theorem; Tverberg's theorem; COLORFUL SIMPLICIAL DEPTH; THEOREM; FAMILIES; FIELDS; SETS;

D O I：

10.1007/s00454-012-9439-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we give sufficient conditions for a compactum in a"e (n) to have Carath,odory number less than n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath,odory theorem and give a Tverberg-type theorem for families of convex compacta.

引用

页码：783 / 792

页数：10

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