集值映射空间的度量化  

Metrization of Multifunction Spaces

作　　者：李祖泉[1] 

机构地区：[1]杭州师范大学理学院数学系,杭州310036

出　　处：《工程数学学报》2008年第3期567-570,共4页Chinese Journal of Engineering Mathematics

基　　金：杭州师范学院科研启动经费资助项目(02010180).

摘　　要：本文研究拓扑空间到一致空间上点紧致的连续集值映射空间在紧开拓扑、一致收敛拓扑、紧致处一致收敛拓扑和度量拓扑等之下它们之间的关系,利用诱导映射和嵌入的方法给出了拓扑空间到实直线上点紧致的连续集值映射空间可度量化的若干等价条件。这些结论将单值连续映射空间上的可度量化结果推广到了点紧致的连续集值映射空间上。In this paper, the relations among the point-compact continuous multifunction spaces under compact-open topology, uniform convergence topology, uniform convergence topology on compacta and metric topology, from a topology space to a metric space, are investigated. Some equivalent results about the point-compact continuous multifunction spaces, which are metrizable from a topological space to the real line with compact-open topology, are obtained by using induced mappings and embedding mappings. These results generalize corresponding results concerning continuous single-valued function spaces to the point-compact continuous multifunction spaces.

关 键 词：集值映射 紧开拓扑 紧致处一致收敛拓扑 一致收敛拓扑 度量拓扑 半紧空间 

分 类 号：O189.1[理学—数学]