| σ(E_1)拓扑的性质和应用 |
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| 引用本文： | 刘浩岳,王清杰.σ(E_1)拓扑的性质和应用[J].河南师范大学学报(自然科学版),1990(1). |
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| 作者姓名： | 刘浩岳 王清杰 |
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| 作者单位： | 河南师范大学数学系，河南师范大学数学系 |
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| 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。
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| 关 键 词： | 拓扑向量空间 极拓扑 弱拓扑 |
THE PROPERTIES OF TOPOLOGY σ(E_1)AND ITS APPLICATION |
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| Lia Haoyue,Wang Qingjie.THE PROPERTIES OF TOPOLOGY σ(E_1)AND ITS APPLICATION[J].Journal of Henan Normal University(Natural Science),1990(1). |
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| Authors: | Lia Haoyue Wang Qingjie |
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| Institution: | Lia Haoyue;Wang Qingjie |
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| Abstract: | 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. |
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| Keywords: | topological vector spaces polar topology weak topology |
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