锥度量半连续集值映射的连续性  

Continuity of cone metric semi-continuous set-valued maps

作　　者：夏顺友[1,2] 向淑文[3] 

机构地区：[1]贵州大学计算机科学与信息学院,贵州贵阳550025 [2]贵州师范学院数学与计算机科学学院,贵州贵阳550018 [3]贵州大学教务处,贵州贵阳550025

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第1期119-122,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(11161008);贵州省科学技术基金资助项目(2012GZ71164)

摘　　要：获得从一个完备度量空间到一个正规锥度量空间上的非紧值锥度量半连续集值映射的连续点集的性质,通过构造第二纲集的方法,得到了从完备度量空间到正规锥度量空间上的不具紧值的锥度量上(下)半连续集值映射的下(上)半连续点构成的集合是定义域的稠密剩余集,即锥度量上(下)半连续集值映射是通有下(上)半连续的或者说是通有连续的.也即是说在Baire纲意义下锥度量半连续集值映射在绝大多数点处是连续的,或者说是"基本上"连续的.该结果对一些非线性问题解的通有稳定性研究条件的减弱提供了一定的理论指导.In order to obtain the properties of continuous points for the cone metric upper semi-continuous and the cone metric lower semi-continuous maps without any compact value from a complete metric space onto a normal cone metric space, the authors prove that the set of continuous points for the cone metric upper semi-continuous and the cone metric lower semi-continuous maps without any compact value from a complete metric space onto a normal cone metric space is dense and residual set in domain by constructing the second category set. In other words, the cone metric upper and lower semi-continuous set-valued maps are generic cone lower and upper semi-continuous, that is, they are generic continuous, or, in the sense of Baire category, cone metric semi-continuous maps are continuous at ＂most＂ points, or, ＂almost＂ continuous. The study has a theoretical reference value for the weakening of generic stabilities conditions of some nonlinear problems.

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

分 类 号：O177.91[理学—数学]