(X,σ(X,Y))可度量化的充要条件

A NECESSARY AND SUFFICIENT CONDITION OF (X,σ(X,Y)) BEING METRIZABLE

(x,y)是对偶空间,x按弱拓扑σ(X,Y)成局部凸空间,本文证明(X,σ(X,Y))可度量化的充要条件是Y的Hamel维至多可列.

Let (X,Y) be pairing linear space,then (X,σ(.X,Y)) is a locally convex linear topological space. In this paper we prove that (X,σ(.X,Y)) is Metrizable if and only if the Hamel dimension of Y is finite or countable.