线性拓扑的泛函表示

The Fuenctional Representation of Topological Vector Space

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.