到锥度量空间上的半连续集值映射的连续性  

Continuity properties of semi-continuous maps with set-value onto cone metric space

作　　者：夏顺友[1] 黄南京[2] 

机构地区：[1]贵州师范学院数学与计算机科学学院,贵州贵阳550018 [2]四川大学数学学院,四川成都610064

出　　处：《辽宁工程技术大学学报（自然科学版）》2012年第2期280-283,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(10561003)

摘　　要：为了获得到锥度量空间的上半连续和下半连续集值映射的连续点所具有的性质,通过构造第二纲集的方法,得到了到锥kR定义的锥度量空间kR的上半连续和下半连续紧值集值映射的连续点构成的集合是定义域中的剩余集.若定义域是Baire空间或完备度量空间,其连续点构成的集合还是稠密的,此时称到锥kR定义的锥度量空间kR的紧值上半连续和下半连续集值映射是通有连续的,也即是说在Baire纲意义下,此时的半连续集值映射在绝大多数点处是连续的,或者说基本上是连续的.该结果对集值分析理论和稳定性问题的研究有一定的理论参考价值和应用指导意义.In order to achieve the properties of continuous points for the upper-semi-continuous and the lower-semi-continuous maps onto cone metric space,this paper proves that the set of continuous points of upper semi-continuous and lower semi-continuous set-valued maps onto cone metric space defined over Rk by cone R+k is residual set in domain by constructing the second category set.In addition,its continuous points set is a dense set if the domain is in Baire space or complete metric space,and the upper semi-continuous and lower semi-continuous set-valued maps onto cone metric space defined over Rk by cone R+k are called generic continuous maps.In other words,these semi-continuous maps are almost continuous in the sense of Baire category,or its non-continuous points are'very small' in the topological sense(the first category).This result has some theoretical reference value for the theory of correspondences and has some guidance in studying stability problems.

关 键 词：集值映射 上半连续 下半连续 通有连续 剩余集 锥度量 锥度量空间 Baire空间 

分 类 号：O177.91[理学—数学]