The intersection properties of generalized Helly families for inverse limit spaces

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• 作者：F.H. Ghane ; Hadi Pass ; ideh ; Hamid Torabi
• 关键词：52A35 ; 54H25 ; 47H10
• 刊名：Topology and its Applications
• 出版年：2013
• 出版时间：15 August, 2013
• 年：2013
• 卷：160
• 期：13
• 页码：1557-1565
• 全文大小：237 K

文摘

The aim of this paper is to discuss the intersection properties of generalized Helly families for topological spaces and inverse limit spaces. This concept is a generalization of Helly family. A generalized Helly family is a countable family of ¡Þ-connected subsets of a topological space X satisfying the following conditions: the intersection of each finite subfamily is ¡Þ-connected; and the intersection of each proper subfamily is nonempty.

In , Kulpa (1997) extended the Helly convex-set theorem onto topological spaces in terms of Helly families. Here, we improve his result. We show that if is a generalized Helly family of compact subsets of a topological space X and is a countable covering of X with , for each , then is nonempty.