A Helly-type theorem for higher-dimensional transversals

被引：4
|
作者：
Aronov, B
Goodman, JE
Pollack, R
机构：
[1] Polytech Univ, Brooklyn, NY 11201 USA
[2] CUNY City Coll, New York, NY 10031 USA
[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA
来源：
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2002年 / 21卷 / 03期
基金：
美国国家科学基金会;
关键词：
Helly-type theorem; geometric transversal theory; k-unbounded; convex sets; k-transversal;
D O I：
10.1016/S0925-7721(01)00025-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that a collection of compact convex sets of bounded diameters in R-d that is unbounded in k independent directions has a k-flat transversal for k < d if and only if every d + I of the sets have a k-transversal. This result generalizes a theorem of Hadwiger(-Danzer-Grunbaum-Klee) on line transversals for an unbounded family of compact convex sets. It is the first Helly-type theorem known for transversals of dimension between 1 and d - 1. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：177 / 183
页数：7
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