拓扑空间子集的最小开集和最大闭集  

Smallest Open Set and Largest Closed Set of a Subset of Topological Space

作　　者：张可秀[1] 

机构地区：[1]漳州师范学院数学与信息科学系,福建漳州363000

出　　处：《大学数学》2011年第5期39-41,共3页College Mathematics

摘　　要：讨论对于拓扑空间子集A是否存在包含A的最小开集和是否存在包含于A的最大闭集问题,证明了拓扑空间X是一个T1空间之充分且必要条件是,对于X的每一个子集A,X中存在包含A的最小开集(存在包含于A的最大闭集)当且仅当A是X的开集(闭集),同时给出几个例子说明了定理的条件.This paper discusses the smallest open set and largest closed set in a subset of topological space,and show that if X is a T space ,and A is a subset of X, then there exists the smallest set containing A in the space （ the largest closed set contained in A ） if and only if A is a open set（closed set）. Several examples are giving at the same time to explain the conditions of the theorems.

关 键 词：拓扑 最小开集 最大闭集 T1空间 

分 类 号：O189.1[理学—数学]