点态性质与一致性质的一个新关系  

A New Relation Between the Pointwise and Uniform Properties

作　　者：蔡龙生[1] 吴定平[1] 史沧红[1] 

机构地区：[1]成都信息工程学院应用数学学院,四川成都610225

出　　处：《成都信息工程学院学报》2014年第2期195-198,共4页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(11171046)

摘　　要：为了研究点态性质和一致性质之间的关系,应用紧性性质在拓扑意义下得到逐点有界性质蕴含一致有界性质的结论,并将其推广到连续函数族的情况.基于Baire定理,得到完备度量空间中的逐点收敛性质可导出一致有界性质的结论.In order to study the relations between the pointwise and uniform properties,we apply the compactness to obtain the result that the pointwise boundedness implies the uniform boundedness under the sense of topology,and then we extend it to the case of a family of continuous functions under certain conditions.Based on the famous Baire＇s theorem,we also verify the assertion that pointwise convergence can deduce the pointwise boundedness in complete metric spaces.

关 键 词：基础数学 泛函分析 完备度量空间 紧集 逐点有界性 一致有界性 EGOROFF定理 

分 类 号：O174.12[理学—数学]