摘要
应用非标准分析法研究线性拓扑空间中的若干性质.首先,在拓扑空间中,对集合的稠密性和无处稠密性进行非标准刻画.其次,给出映射连续、上半连续、下半连续的非标准特征.最后,在线性拓扑空间中,应用非标准分析的方法研究凸集、凸包的性质.
Some properties in linear topological space are studied by nonstandard analysis.First-ly,the nonstandard characterizations of denseness and nowhere denseness of set in topological space are obtained.Then the nonstandard characterizations of continuity,upper semicontinuity and lower semicontinuity of mapping are shown.Finally,some properties of convex set and con-vex hull are studied by nonstandard analysis in linear topological space.
出处
《纺织高校基础科学学报》
CAS
2016年第1期123-127,共5页
Basic Sciences Journal of Textile Universities
基金
陕西省自然科学基金资助项目(2007A12)
陕西省教育厅专项科研基金项目(2013JK0574)
西安建筑科技大学人才科技基金项目(RC1239)
关键词
线性拓扑空间
单子
上半连续
凸集
凸包
linear topological space
monad
upper semicontinuity
convex set
convex hull
