| Strong Minkowski Separation and Co-Drop Property |
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| 作者姓名： | Jing Hui QIU |
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| 作者单位： | Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （10571035） |
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| 摘 要： |
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| 关 键 词： | 局部凸空间 强闵可夫斯基分离 弱可数紧集 下落特征 |
| 收稿时间： | 2006-02-22 |
| 修稿时间： | 2007-01-16 |
Strong Minkowski Separation and Co-Drop Property |
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| Jing Hui QIU.Strong Minkowski Separation and Co-Drop Property[J].Acta Mathematica Sinica,2007,23(12):2295-2302. |
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| Authors: | Jing Hui Qiu |
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| Institution: | (1) Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China |
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| Abstract: | In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact. |
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| Keywords: | drop property co-drop property locally convex space strong Minkowski separation weakly countably compact set |
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