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Strong Minkowski Separation and Co-Drop Property 被引量：2

Strong Minkowski Separation and Co-Drop Property
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摘要 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. 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.
作者 Jing Hui QIU
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第12期2295-2302,共8页 数学学报（英文版）
基金 National Natural Science Foundation of China(10571035)
关键词 drop property co-drop property locally convex space strong Minkowski separation weakly countably compact set drop property, co-drop property, locally convex space, strong Minkowski separation, weakly countably compact set
分类号 O174.13 [理学—基础数学]
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参考文献26

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Acta Mathematica Sinica,English Series
2007年 第12期

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