| 正规分离两个集的新概念及其属性 |
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| 引用本文： | 王琪,潘文熙. 正规分离两个集的新概念及其属性[J]. 中山大学学报(自然科学版), 2000, 39(6): 20-25 |
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| 作者姓名： | 王琪 潘文熙 |
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| 作者单位： | 1. 中山大学教育学院，广东广州 510275
2. 暨南大学数学系，广东广州 510632 |
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| 摘 要： | 引入了正规分离并证明了它的存在性，从而摆脱了原先生定理须预先假设存在近渡点的限制，得到了完善化，与此同时又建立了正规分离的一系列性质。比如联系近渡点及最近点对的关系，正规分离的唯一性等，改进了著名的Ｍａｚｕｒ定理和Ｅｉｄｅｌｌｅｉｔ分离定理。
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| 关 键 词： | 正规分离 近渡点 最近点对 贴支承 存在性 凸集 |
| 文章编号： | 0529-6579(2000)06-0020-06 |
| 修稿时间： | 2000-01-19 |
New Concept of Normal Separation of Two Sets and Its Properties |
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| WANG QiSchool of Education,Zhongshan University,Guangzhou ,China,PAN Wen|xi. New Concept of Normal Separation of Two Sets and Its Properties[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2000, 39(6): 20-25 |
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| Authors: | WANG QiSchool of Education Zhongshan University Guangzhou China PAN Wen|xi |
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| Affiliation: | WANG QiSchool of Education,Zhongshan University,Guangzhou 510275,China,PAN Wen|xi |
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| Abstract: | The concept of normal separation (NS) of two convex sets is introduced.Its existence is proved.Then the restricting condition,existence of nearest cross point,is relaxed.And then some properties of NS are established,e^g. uniqueness of NS;the relations between NS and nearest cross pionts,etc.These generalize the well known Eidelheit separation theorem and Mazur theorem extensively. |
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| Keywords: | normal separation nearest cross point proximity pair supporting hyperplane adherent supporting |
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