非拓扑向量空间的拟拓扑向量空间  

Quasi-topological vector space of non-topological vector space

作　　者：杨忠强 郑秋楠 YANG Zhongqiang;ZHENG Qiunan(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）》2024年第2期87-93,共7页Journal of Minnan Normal University：Natural Science

基　　金：国家自然科学基金(11971287)。

摘　　要：拟拓扑向量空间是在向量空间赋予一个拓扑使其满足数乘联合连续,加法分离变量连续的空间,给出生成非拓扑向量空间的拟拓扑向量空间的方法,由此可以得到仿紧的拟拓扑向量空间但不是拓扑向量空间.A quasi-topological vector space is a vector space equipped with a topology satisfying the conditions that the scalar multiplication is jointly continuous and the additive separation of variables is continuous.Based on this,the method of generating quasi-topological vector space of non-topological vector space is given.From this,we obtain a quasi-topological vector space which is paracompact but not a topological vector space.

关 键 词：拓扑向量空间 拟拓扑向量空间 仿紧 

分 类 号：O189[理学—数学]