| 半连续函数通有连续性的一个推广 |
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| 引用本文： | 吉丽超,刘美,陆学勇,向淑文.半连续函数通有连续性的一个推广[J].贵州大学学报(自然科学版),2007,24(3):234-236. |
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| 作者姓名： | 吉丽超 刘美 陆学勇 向淑文 |
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| 作者单位： | 贵州大学,理学院数学系,贵州,贵阳,550025 |
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| 摘 要： | 令X为度量空间,将定义在X上的下半连续有上界、上半连续有下界的实值函数f转化为集值映射F,通过Aubin定理,证明F在X上通有连续,进而证明f在X上通有连续,最后给出了定义在拓扑空间上的半连续实值函数通有连续性的一个直接证明。
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| 关 键 词： | 下半连续 集值映射 闭映射 剩余集 通有连续 |
| 文章编号： | 1000-5269（2007）03-0234-03 |
| 修稿时间： | 2007-04-04 |
A Generalization of Generic Continuity of Semicontinuous Functions |
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| JI Li-chao,LIU Mei,LU Xue-yong,XIANG Shu-wen.A Generalization of Generic Continuity of Semicontinuous Functions[J].Journal of Guizhou University(Natural Science),2007,24(3):234-236. |
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| Authors: | JI Li-chao LIU Mei LU Xue-yong XIANG Shu-wen |
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| Institution: | Dept. of Math, College of science, Guizhou University, Guiyang, Guizhou 550025, China |
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| Abstract: | Let X be a metric space.In this paper,author translate lower(upper) semicontinuous bounded above(below) real-valued function f on X into set-valued mapping.F From the Aubin theorem,it is easy to prove F is generic continuous on X,then the generic continuity of f on X can be derived.In the end,author give a direct prove of the generic continuity of semicontinuous real-valued function which is defined on topological space. |
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| Keywords: | lower semicontinuous set-valued mapping closed mapping residual set generic continuous |
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