摘要
以拓扑空间上的半开(闭)集和θ-开(闭)集为基础,给出了超空间上集值映射的弱上半连续和弱下半连续的新定义,分别以拓扑空间、度量空间和赋范空间作为值域空间讨论了弱上(下)半连续的若干等价条件,证明弱上(下)半连续集值映射是弱连续集值映射与半连续集值映射的推广和扩充,给出了弱下半连续集值映射的子集网式的特征性质,最后给出了闭包映射和凸包映射成为弱上(下)半连续集值映射的条件.
In this paper, the new definitions of weakly upper and weakly lower semi-continuous set-valued mappings on hyperspace are given by semi-open(closed) sets and θ -open(closed) sets in topological space. Some equivalent conditions of this kind of set-valued mappings are discussed when range spaces are topological spaces, metric spaces and normable spaces respectively. Weakly upper(lower ) semi-continuous set-valued mappings are both the generalization of weak continuous set-valued mappings and semi-continuous set-valued mappings are proved, and the characteristic properties of weakly lower semi-continuous set-valued mappings are given by nets of subsets. Finally, the conditions of closure mappings and convex mappings to be weakly upper (lower )semi-continuous set-valued mappings are given.
出处
《西南民族大学学报（自然科学版）》
CAS
2009年第3期414-418,共5页
Journal of Southwest Minzu University(Natural Science Edition)
基金
四川省教育厅科研基金资助项目(2006C041)
关键词
拓扑空间
超空间
集值映射
半开(闭)集
θ-开(闭)集
闭包映射
凸包映射
弱半连续性
topological space
hyper space
set-valued mapping
semi-open(closed) set
θ-open(closed) set
closure mapping
convex mapping
weakly semi-continuity
