集值映射空间在紧开拓扑下的N性质

摘要

本文研究了点紧连续集值映射族在紧开拓扑下的N性质.利用cs-σ网方法获得了如下结果:若X是(N)o空间,Y是(N)空间,则Ck(X,Y)是(N)空间.该结论将J.A.Guthrie关于单值连续映射空间的结论推广到了集值映射空间上,并且改进了相关结论.%This paper discusses the (N) property of point-compact continuous multifunction spaces with compact-open topology.By using a cs-σ-network,it obtains that if X is an (N)0-space,Y is an (N)-space,then the point-compact continuous multifunction space with compact-open topology is an (N)-space.This generalizes J.A.Guthrie's results to wider topological space,and improves relevant conclusions.