关于拓扑空间中一些点集的注记  

Notes about some point sets in topological space

作　　者：史学青[1] 金渝光[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《长春大学学报》2009年第8期67-68,共2页Journal of Changchun University

基　　金：重庆市教委科学研究项目(05JWSK054)

摘　　要：本文首先给出了拓扑空间中的一个集合为闭集的充要条件,从而进一步得到拓扑空间中的一个集合的闭包和边界集必为闭集并且它的闭包是包含着这个集合的最小的闭集。其次我们知道在一般的度量空间中一个集合的导集必是闭集,但是在一般拓扑空间中此结论不一定成立,所以本文主要给出了在拓扑空间中一个集合的导集为闭集的的充分条件和充分必要条件。Firstly, this article gives a sufficient and necessary condition when a set is a closed one in a topological space, than gets a closure in a topological space and a closed set whose closure is the smallest of all closed sets that contain it when the border set must be a closed one. Secondly, we knew that a derived set must be a closed one in the general metric space, but this conclusion is not necessarily proper in the general topological space, therefore this article mainly gives a sufficient and necessary condition when the derived set is a closed one in the topological space.

关 键 词：导集 闭包 内部 边界集 闭集 T1 空间 

分 类 号：O19[理学—数学]