无穷维线性赋范空间的连续性  

Continuity of infinite dimensional linear normed space

作　　者：赵颖 ZHAO Ying(Sichuan Technology and Business University,Chengdu 610000,China)

机构地区：[1]四川工商学院,成都610000

出　　处：《计算机应用文摘》2024年第12期123-125,共3页Chinese Journal of Computer Application

摘　　要：作为分析学中最基本的概念之一,映射的连续性与空间的拓扑紧密相关。人们所讨论的映射基本在无穷维线性赋范空间内,其中包含强拓扑、弱拓扑以及弱*拓扑等,能够导出许多不同的连续性。在研究和处理各类具体问题时,采用适当的连续性常常会事半功倍。文章主要介绍了几种常见的连续性及其之间的联系。As one of the most fundamental concepts in analysis,the continuity of mapping is closely related to the topology of space.The mappings discussed by people are basically in infinite dimensional linearly normed spaces,which include strong topology,weak topology,and weak*topology,and can derive many different types of continuity.When studying and dealing with various specific problems,adopting appropriate continuity often yields twice the result with half the effort.The article mainly introduces several common continuity and their connections.

关 键 词：连续性 次连续 弱连续 半连续 强连续 

分 类 号：O177[理学—数学]