PIERCING CONVEX-SETS

被引:8
作者
ALON, N
KLEITMAN, DJ
机构
[1] BELLCORE,MORRISTOWN,NJ 07960
[2] MIT,DEPT MATH,CAMBRIDGE,MA 02139
关键词
D O I
10.1090/S0273-0979-1992-00304-X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A family of sets has the (p, q) property if among any p members of the family some q have a nonempty intersection. It is shown that for every p greater-than-or-equal-to q greater-than-or-equal-to d + 1 there is a c = c(p, q, d) < infinity such that for every family F of compact, convex sets in R(d) that has the (p , q) property there is a set of at most c points in R(d) that intersects each member of F. This extends Helly's Theorem and settles an old problem of Hadwiger and Debrunner.
引用
收藏
页码:252 / 256
页数:5
相关论文
共 21 条
[1]  
ALON N, UNPUB COMBIN PROB CO, V1
[2]  
ALON N, IN PRESS ADV MATH
[3]  
Alon N., 1985, EUROP J COMB, V6, P211
[4]   A GENERALIZATION OF CARATHEODORYS THEOREM [J].
BARANY, I .
DISCRETE MATHEMATICS, 1982, 40 (2-3) :141-152
[5]  
Danzer L., 1963, P S PURE MATH, V7, P101, DOI [DOI 10.1090/PSPUM/007/0157289, 10.1090/pspum/007, DOI 10.1090/PSPUM/007]
[6]  
Dolnikov V.L., 1972, SIB MATH J, V13, P886
[7]  
ECHHOFF J, IN PRESS HDB CONVEX
[8]  
Eckhoff J., 1985, GEOMETRIAE DEDICATA, V19, P217
[9]   INTERSECTIONAL PROPERTIES OF CERTAIN FAMILIES OF COMPACT CONVEX-SETS [J].
FULLBRIGHT, BE .
PACIFIC JOURNAL OF MATHEMATICS, 1974, 50 (01) :57-62
[10]  
Grunbaum B., 1959, PORT MATH, V18, P155