| 集值映射空间在紧开拓扑下的$\aleph_0$性质 |
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| 引用本文： | 李祖泉.集值映射空间在紧开拓扑下的$\aleph_0$性质[J].数学研究及应用,2007,27(4):933-938. |
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| 作者姓名： | 李祖泉 |
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| 作者单位： | 杭州师范学院数学系, 浙江\ 杭州 310036 |
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| 基金项目： | 杭州师范学院科研启动经费资助(02010180). |
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| 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.
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| 关 键 词： | 集值映射 紧开拓扑 伪基 $\aleph_{0}$空间. |
| 文章编号： | 1000-341X（2007）04-0933-06 |
| 收稿时间： | 2005/4/26 0:00:00 |
| 修稿时间： | 2005-04-26 |
$\aleph_{0}$-Property of Multifunction Spaces under Compact-Open Topology |
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| LI Zu-quan.$\aleph_{0}$-Property of Multifunction Spaces under Compact-Open Topology[J].Journal of Mathematical Research with Applications,2007,27(4):933-938. |
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| Authors: | LI Zu-quan |
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| Institution: | 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$^{1]}$. |
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| Keywords: | multifunction compact-open topology pseudo-base $\aleph_{0}$-space |
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