A Helly-type theorem for countable intersections of starshaped sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A Helly-type theorem for countable intersections of starshaped sets

Authors:	Marilyn Breen

Institution:	(1) Department of Mathematics, University of Oklahoma, Norman, Oklahoma, 73019, U.S.A

Abstract:	Let k and d be fixed integers, 0kd, and let $\mathcal{K} = \{ k_\alpha :\alpha {\text{ in some index set}}\}$ be a collection of sets in $\mathbb{R}^d .$ If every countable subfamily of $\mathcal{K}$ has a starshaped intersection, then $\cap \{ k_\alpha :k_\alpha {\text{ in }}\mathcal{K}\}$ is (nonempty and) starshaped as well. Moreover, if every countable subfamily of $\mathcal{K}$ has as its intersection a starshaped set whose kernel is at least k-dimensional, then the kernel of $\cap \{ k_\alpha :k_\alpha {\text{ in }}\mathcal{K}\}$ is at least k-dimensional, too. Finally, dual statements hold for unions of sets.Received: 3 April 2004

Keywords:	Primary 52A30 52A35
本文献已被 SpringerLink 等数据库收录！