一类S闭空间

J4 ›› 2012, Vol. 47 ›› Issue (2): 115-118.

一类S闭空间

张夏苇¹, 孔庆钊^2*, 陈海燕³

1. 厦门理工学院数学系,福建厦门 361021;
2. 集美大学理学院, 福建厦门 361021;
3. 广西大学数学与信息科学学院, 广西南宁 530004

收稿日期:2010-10-26 出版日期:2012-02-20 发布日期:2012-12-24
通讯作者: 孔庆钊(1978- ), 男, 讲师, 硕士, 研究方向为一般拓扑学. Email: kongqingzhao@163.com
作者简介:张夏苇(1981- ), 女, 讲师, 硕士研究生, 研究方向为一般拓扑学. Email: xiawzhang@163.com
基金资助:
福建省自然科学基金资助项目(2010J05010)；福建省教育厅项目(JB09202)；广西自然科学基金资助项目（桂科自0728035）

On a kind of S-closed spaces

ZHANG Xia-wei¹， KONG Qing-zhao^2*， CHEN Hai-yan³

1. Department of Mathematics and Physics, Xiamen University of Technology, Xiamen 361021, Fujian, China；
2. College of Mathematics and Physics, Jimei University, Xiamen 361021, Fujian, China；
3. College of Mathematics and Information Science, Guangxi University, Nanning 530004, Guangxi, China

Received:2010-10-26 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

摘要：

讨论了S闭空间的性质,证明了(1)局部S闭空间是半正则遗传的;(2)如果A是正则开集,则A是X的局部S闭子空间当且仅当A相对X是局部S闭的;(3)每一T₂的最小局部S闭空间是S闭空间。

关键词: 局部S闭空间;半正则集;半开集

Abstract:

The properties extending S-closed spaces are discussed. It is shown that (1) every semi-open regular subspace of a locally S-closed space is locally S-closed. (2)If A is a regular open subset of X, then A is locally S-closed if and only if A is locally S-closed relative to X. (3) Every T2 minimal-locally-S-closed space is Sclosed.

Key words: locally S-closed spaces; semi-regular set; semi-open set

张夏苇1, 孔庆钊2*, 陈海燕3. 一类S闭空间[J]. J4, 2012, 47(2): 115-118.

ZHANG Xia-wei1， KONG Qing-zhao2*， CHEN Hai-yan3. On a kind of S-closed spaces[J]. J4, 2012, 47(2): 115-118.

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