辽宁工程技术大学学报（自然科学版）Issue(2)：280-283,4.
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
摘要
Abstract
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Key words
set-valued map/ upper semi-continuity/ lower semi-continuity/ generic continuity/ residual set/ cone metric/ cone metric space/ Baire space分类
数理科学引用本文复制引用
夏顺友,黄南京..到锥度量空间上的半连续集值映射的连续性[J].辽宁工程技术大学学报（自然科学版）,2012,(2):280-283,4.基金项目
国家自然科学基金资助项目(10561003) （10561003）
