某些局部凸空间上相对弱紧集，相对弱列紧集，相对弱可数紧集的关系

Relation of Relatively weakly Compact,Relatively weakly Sequentially Compactand Relatively,Weakly Countable Compact on Some Locslly Convex Spaces

对可分离的局部凸空间（Ｘ，τ），本文建立了相应的局部凸空间（Ｑｘ，Ｔｘ），利用它证明了当（Ｘ，τ）满足某些条件时（赋范空间满足这些条件），ＥＸ相对弱紧Ｅ相对弱列紧Ｅ相对弱可数紧，从而推广了Ｅｂｅｒｌｅｉｎ等人的工作，证明了在空间Ｄ（Ｒ￣ｎ），（Ｒ￣ｎ）和Ｄ＿（ＬＰ），１＜ｐ＜∞上前述三种弱紧性等价．

Let(X,τ)is a T_2 locally convex space. we can produce a new T_2 locally convexspace(Q_x,T_x)which depends on(X,τ). Using(Q_x,T_x),we have proved that if(X,τ)sufficessome conditions(we know normed space suffices these conditions),then, for E X,we have:Eis a relatively weakly compact set E is a relatively weakly sequentially compact set E is arelatively weakly countable compact set.As an example,we have proved that the basic function space D(R￣n)suffices these conditions,thelefore,the mentioned three weakly compacts are equavalence on D(R￣n).