集值映射空间中的紧*拓扑  

The compact * -topology of multifunction spaces

作　　者：李祖泉[1] 王久晶 

机构地区：[1]杭州师范学院数学系,浙江杭州310036 [2]杭州师范学院图书馆,浙江杭州310036

出　　处：《黑龙江大学自然科学学报》2005年第6期826-829,833,共5页Journal of Natural Science of Heilongjiang University

基　　金：杭州师范学院科研启动经费资助项目

摘　　要：在集值映射空间引入了新的拓扑结构,即紧*拓扑.在值域空间是一致空间下给出了上半*连续(下半*连续)的充分条件,在值域空间是强一致空间下给出了上半*连续(下半*连续)的充分必要条件,在点紧连续映射族上证明了紧*拓扑细于紧开拓扑,在连续映射族上紧致处一致收敛拓扑细于紧*拓扑.A kind of topology, e. g. , compact ＊ - topology, was introduced. When range space is uniform space, a sufficient condition about upper semi - ＊ - continuous and lower semi - ＊ - continuous multifunction was given. When range space is strong uniform space, a sufficient and necessary condition about upper semi - ＊ - continuous and lower semi - ＊ - continuous multifunction was given. It was proved that compact ＊ - topology is finer than the compact - open topology of muhifunction spaces when every muhifunction was point compact, and that uniform convergence topology on a family of compact sets is finer than the compact ＊ - topology of multifunction spaces.

关 键 词：强一致空间 紧开拓扑 一致收敛拓扑 点态收敛拓扑 紧＊拓扑 

分 类 号：O189.1[理学—数学]