期刊信息
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- 刊名: 河北师范大学学报(自然科学版)Journal of Hebei Normal University (Natural Science)
- 主办: 河北师范大学
- ISSN: 1000-5854
- CN: 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
紧凸集族横截定理的注记
-
1. 河北师范大学, 数学与信息科学学院, 河北, 石家庄, 050016;
2. 衡水师范专科学校数学系, 河北, 衡水, 053000 -
DOI:
A Note on Line Transversal Theorem of a Family of Compact Convex Sets
摘要/Abstract
摘要:
Helly定理是凸集理论的三大基本定理之一,紧凸集族的横截定理是Helly定理的重要推广,具有很强的应用性。现给出一反例说明紧凸集族的横截定理证明过程中存在疏漏,利用一般 Helly定理和凸集性质对紧凸集族横截定理的原证明进行修正。
Abstract:
Helly theorem is one of the three fundamental theorems in convex theory.The line transversal theorem of a family of compact convex sets is one of its important generalizations,and is widely used.A counter example is given to show that there is a gap in the proof of the line transversal theorem of a family of compact convex sets. The proof is corrected by using general Helly theorem and convex pro perties.
关键词
Key words:
compact set
;
convex set
;
line transversal