| 关于两个Cartesian闭范畴交的一点注记 |
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| 引用本文： | 刘菡 贺伟. 关于两个Cartesian闭范畴交的一点注记[J]. 南京师大学报(自然科学版), 2005, 28(4): 13-17 |
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| 作者姓名： | 刘菡 贺伟 |
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| 作者单位： | [1]南京师范大学数学与计算机科学学院,江苏南京210097 [2]徐州师范大学数学系,江苏徐州221116 |
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| 基金项目： | 国家自然科学基金资助项目（10331010）. |
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| 摘 要： | 讨论了关于双Scott拓扑的一些性质．证明了范畴BICONT（即以双连续格为对象，以双Scott连续映射为态射的范畴）作为两个Cartesian闭范畴BICONTS（即以双连续格为对象，以Scott连续映射为态射的范畴）和BICONTSop（即以双连续格为对象，以对偶Scott连续映射为态射的范畴）的交范畴不是Cartesian闭范畴．
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| 关 键 词： | 双Scott拓扑 双连续格 双Scott连续映射 对偶Scott连续映射 Cartesian闭范畴 |
| 文章编号： | 1001-4616（2005）04-0013-05 |
| 收稿时间： | 2005-05-28 |
| 修稿时间： | 2005-05-28 |
A Remark on the Meet of Two Cartesian Closed Categories |
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| Liu Han, He Wei. A Remark on the Meet of Two Cartesian Closed Categories[J]. Journal of Nanjing Normal University(Natural Science Edition), 2005, 28(4): 13-17 |
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| Authors: | Liu Han He Wei |
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| Affiliation: | 1. School of Mathematics and Computer Science, Nanjing Normal University, 210097, Nanjing, China; 2. Department of Mathematics, Xuzhou Normal University, 221116, Xuzhou, China |
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| Abstract: | In this paper,we discuss some properties of biscott topology.Then we prove that the category BICONT(i.e.the category whose objects are bicontinuous lattices and whose morphisms are biscott continuous maps),as the intersectional category of two Cartesian closed categories BICONT_S(i.e.the category whose objects are bicontinuous lattices and whose morphisms are scott continuous maps) and BICONT_(S~(op))(i.e.the category whose objects are bicontinuous lattices and whose morphisms are dual scott continuous maps) is not a Cartesian closed category. |
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| Keywords: | biscott topology bicontinuous lattice biscott continuous map dual scott continuous map Cartesian closed category |
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