集值映射空间在紧开拓扑下的$\aleph_0$性质

$\aleph_{0}$-Property of Multifunction Spaces under Compact-Open Topology

中文关键词:  集值映射  紧开拓扑  伪基  $\aleph_{0}$空间.

英文关键词:multifunction  compact-open topology  pseudo-base  $\aleph_{0}$-space.

中文摘要:

      本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若$X,Y$为$\aleph_0$空间,则$X$到$Y$上的点紧致的连续集值映射族依紧开拓扑是$\aleph_{0}$空间,从而将Michael$^{[1]}$的结论推广到更大的映射空间类上.

英文摘要:

      In this paper, we discuss some properties of the point-compact continuous multifunction spaces with compact-open topology and show that if $X, Y$ are $\aleph_{0}$-space, then the point-compact continuous multifunction space with compact-open topology is an $\aleph_{0}$-space, which is a generalization of a corresponding result concerning continuous single-valued function spaces proved by E.Michael$^{[1]}$.