摘要
在这篇文章中,我们得到如下结果:任何拓扑线性空间的拓扑都可由一族“广义”γ-次加弱半范族唯一确定,(γ>0),然后我们利用“广义”γ-次加弱半范族来讨论拓扑线性空间的一些性质,作为上面结果的应用,我们指出,赋β-范空间(0<β<1)的拓扑可以用另一泛函——γ-次加弱范来确定。
In this paper,we come to the conclusion that the topology of every topological vector space can be determined by a family of genera- lized γ-subadditive weak seminorms(γ>0).Then by using of it we stu- died the properties of topological vector spaces.As one of the applications- of above results,we obtain that the topology of a β-norm space(0<β<1) can be determined by another functional——γ-subadditive weak norm.
出处
《中国民航学院学报》
1990年第2期44-49,共6页
Journal of Civil Aviation University of China
关键词
拓扑
线性空间
泛函分析
the family of generalized γ-subadditive weak seminorms
Minkowski fcnction
γ-subadditive weak norm