| 集值映射下半连续的三个充要条件 |
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| 引用本文： | 王莉婕.集值映射下半连续的三个充要条件[J].湖州师范学院学报,2004,26(2):26-28. |
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| 作者姓名： | 王莉婕 |
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| 作者单位： | 湖州师范学院,理学院,浙江,湖州,313000 |
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| 摘 要： | 用具体例子揭示了集值映射上半连续和下半连续本质的不同性，给出了集值映射下半连续的三个充要条件和相应的证明，使得集值映射的连续性理论在稳定性的应用中更加灵活方便，在某些情况下也可以作为集值映射下半连续的判定准则。
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| 关 键 词： | 集值映射 上半连续 下半连续 |
| 文章编号： | 1009-1734(2004)02-0026-03 |
| 修稿时间： | 2004年3月13日 |
Three Sufficient and Necessary Conditions for Lower Semi-continuity of Set-valued Mappings |
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| WANG Lijie.Three Sufficient and Necessary Conditions for Lower Semi-continuity of Set-valued Mappings[J].Journal of Huzhou Teachers College,2004,26(2):26-28. |
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| Authors: | WANG Lijie |
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| Abstract: | The most essential and important character in semicontinuity of setvalued mappings is its lower semicontinuity and upper semicontinuity. By using two concrete examples, this article reveals the essential difference between the two semicontinuities and gives three sufficient and necessary conditions for lower semicontinuity of setvalued mappings and the relative proofs, which can convenience the application of semicontinuity theory in stability area and sometimes we can look on the three conditions as the judgment of lower semicontinuity. |
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| Keywords: | set-valued mapping lower semi-continuity upper semi-continuity |
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