TRANSVERSALS OF FAMILIES OF SETS IN R(N) AND A CONNECTION BETWEEN THE HELLY AND BORSUK THEOREMS

被引：12
作者：
DOLNIKOV, VL
机构：
来源：
RUSSIAN ACADEMY OF SCIENCES SBORNIK MATHEMATICS | 1994年 / 79卷 / 01期
关键词：
D O I：
10.1070/SM1994v079n01ABEH003491
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A criterion is obtained for the existence, given a family of convex sets in R(n), of an m-dimensional plane intersecting all members of the family. The results are a generalization of the theorems of Helly, Horn-Klee, and Borsuk. Also presented are applications of these results to the geometry of convex sets and to combinatorics.
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页码：93 / 107
页数：15
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