空间的一特殊点可数族使其为D-空间(英文)  

A Special Point-countable Family That Makes a Space to be a D-space

作　　者：彭良雪[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《数学进展》2008年第6期724-728,共5页Advances in Mathematics（China）

基　　金：Research supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality.

摘　　要：本文给出了空间为D-空间的一充分条件，主要结论如下：如果空间X有一点可数族厂，满足对X的任一子集A X，若A在X中不闭，都存在某点X∈A＼A，使得对X的任一开集U，若X∈U，都存在某个F∈F，使得X∈F U且F∩A≠D，则X是D-空间．由此结论，我们得到一序列空间若有点可数C8^8-网络，则X是D-空间．In this note, we give a sufficient condition that a space to be a D-space. The following is the main conclusion： If a space X has a point-countable family 5r, such that for any set A C X, if A is not closed in X, then there exists some point x ∈ A ／ A, satisfying that for any open set U of X, suppose x ∈ U, there exists some F∈F, such that x∈ F ∪and F∩ A A ≠Φ. Then X is a D-space. By this result, we will know that a sequential space with a point-countable cs^＊-network is a D-space.

关 键 词：D-空间 序列空间 弱基 C8^＊-网络 

分 类 号：O189.1[理学—数学]