$\aleph_{0}$-Property of Multifunction Spaces under Compact-Open Topology
Received:April 26, 2005  Revised:November 26, 2005
Key Words: multifunction   compact-open topology   pseudo-base   $\aleph_{0}$-space.  
Fund Project:the Science and Research Promotional Foundation of Hangzhou Teacher's College (02010180).
Author NameAffiliation
LI Zu-quan Department of Mathematics, Hangzhou Teachers College, Zhejiang 310036, China 
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Abstract:
      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$^{[1]}$.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.04.044
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