| 集值映射空间中的紧*拓扑 |
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| 引用本文： | 李祖泉,王久晶. 集值映射空间中的紧*拓扑[J]. 黑龙江大学自然科学学报, 2005, 22(6): 826-829 |
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| 作者姓名： | 李祖泉 王久晶 |
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| 作者单位： | 杭州师范学院,数学系,浙江,杭州,310036;杭州师范学院,图书馆,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项目 |
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| 摘 要： | 在集值映射空间引入了新的拓扑结构,即紧*拓扑.在值域空间是一致空间下给出了上半*连续(下半*连续)的充分条件,在值域空间是强一致空间下给出了上半*连续(下半*连续)的充分必要条件,在点紧连续映射族上证明了紧*拓扑细于紧开拓扑,在连续映射族上紧致处一致收敛拓扑细于紧*拓扑.
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| 关 键 词： | 强一致空间 紧开拓扑 一致收敛拓扑 点态收敛拓扑 紧*拓扑 |
| 文章编号： | 1001-7011(2005)06-0826-04 |
| 修稿时间： | 2005-02-28 |
The compact * -topology of multifunction spaces |
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| LI Zu-quan,WANG Jiu-jing. The compact * -topology of multifunction spaces[J]. Journal of Natural Science of Heilongjiang University, 2005, 22(6): 826-829 |
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| Authors: | LI Zu-quan WANG Jiu-jing |
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| Affiliation: | LI Zu-quan~1,WANG Jiu-jing~2 |
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| Abstract: | A kind of topology,e.g.,compact *-topology,was introduced.When range space is uniform space,a sufficient condition about upper semi-*-continuous and lower semi-*-continuous multifunction was given.When range space is strong uniform space,a sufficient and necessary condition about upper semi-*-continuous and lower semi-*-continuous multifunction was given.It was proved that compact *-topology is finer than the compact-open topology of multifunction spaces when every multifunction was point compact,and that uniform convergence topology on a family of compact sets is finer than the compact *-topology of multifunction spaces. |
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| Keywords: | strong uniform space compact-open topology uniform convergence topology point-wise convergence topology compact *-topology |
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