具有开点拓扑的函数空间上的基数函数  

A cardinal function on a function space with the open point topology

作　　者：陈结文 张静 CHEN Jiewen;ZHANG Jing(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2020年第2期13-16,共4页Journal of Minnan Normal University：Natural Science

基　　金：国家自然科学基金项目(11801254)。

摘　　要：若X是完全正则空间,1)若X是零维的,f∈C(X)且|f(X)|=κ+,则开点拓扑的特征大于基数κ;2)空间X的π权不超过开点拓扑的伪特征;3)如果X有由非平凡连通集构成的π基ξ且|ξ|≤κ,则开点拓扑的稠密度不超过基数κ;4)如果X有由非平凡连通集构成的π基ξ且|ξ|≤κ并且有一个较粗的度量拓扑,则双点开拓扑的稠密度不超过基数κ.这些结果推广了A.Jinal,R.A.McCoy和S.Kundu的相应结果.It proves that if X is a completely regular space,1)if X is 0-dimensional,f∈C(X)and|f(X)|=κ+,the character of open-point topology is greater than cardinalκ;2)theπ-weight of a space X is less than or equal to the pseudocharacter of the open-point topology;3)if X has aπ-base consisting of nontrivial connected sets,the density of open-point topology is less than or equal to cardinalκ;4)if X has aπ-base consisting of nontrivial connected sets and it has a coarser metrizable topology,the density of bi-point-open is less than or equal to cardinalκ,which improve some results of A.Jinal,R.A.McCoy and S.Kundu.

关 键 词：开点拓扑 双点开拓扑 基数函数 

分 类 号：O189[理学—数学]