关于S-亚紧空间的一些结果  

Some results on the S-metacompact space

作　　者：彭知南 朱培勇[1] PENG Zhi-nan ZHU Pei-yong(School of Mathematical Sciences,UESTC,Chengdu 611731 ,P. R. C.)

机构地区：[1]电子科技大学数学科学学院,四川成都611731

出　　处：《西南民族大学学报（自然科学版）》2016年第6期692-695,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助(11501391)

摘　　要：对S-亚紧空间的一些性质进行研究,得到如下一些结果:(1)拓扑空间X是S-亚紧的当且仅当X的每一个定向开覆盖都有点有限的半开加细.(2)设X,Y是拓扑空间,f:X→Y是完备的优柔映射.如果Y是S-亚紧的,则X也是S-亚紧的.(3)设X是一个S-亚紧空间,如果Y是紧空间,则X×Y也是S-亚紧空间.Some properties of the S-metacompact space are studied. The results are obtained as follows： （1）The topological space X is S-metacompact,if and only if each directed open cover of X has a point finite semi-open refinement. （2）Suppose that X, Y are topological space ,f： X---, Y is perfect irresolute mapping, if Y is S-metacompact, such that X is S-matecompact. （3）Sup- pose Y is an S-matecompact space, if Y is a compact space, then X x Y is also an S-matecomvact svace.

关 键 词：S-亚紧空间 完备映射 优柔映射 定向开覆盖 点有限半开加细 

分 类 号：O189[理学—数学]