σ(E_1)拓扑的性质和应用  

THE PROPERTIES OF TOPOLOGY σ(E_1)AND ITS APPLICATION

作　　者：刘浩岳 王清杰[1] 

机构地区：[1]河南师范大学数学系

出　　处：《河南师范大学学报（自然科学版）》1990年第1期1-4,共4页Journal of Henan Normal University(Natural Science Edition)

摘　　要：在第1节中讨论了σ(E_1)拓扑的性质,主要结果是证明了σ(E_1)和一个极族所导入的极拓扑相等。作为应用,在第2节中证明了自反情况下的Krein—Smulian定理。We have discussed the properties of topology σ(E_1)in section one.The main results are to prove the equality of topology σ(E_1)and a polar topology which are reduced by a polar family.The elements of this polar family are absolutely convex and absorbing(norm)bounded closed subsets of E_1.As the application of σ(E_1),we have shown the excellent Krein-Smulian theorem for reflexive Banach space E.

关 键 词：拓扑向量空间 极拓扑 弱拓扑 

分 类 号：O177.3[理学—数学]