| 笛卡儿闭Domain范畴的两个重要性质 |
| |
| 引用本文： | 刘妮.笛卡儿闭Domain范畴的两个重要性质[J].模糊系统与数学,2006,20(6):28-34. |
| |
| 作者姓名： | 刘妮 |
| |
| 作者单位： | 陕西师范大学,数学与信息科学学院,陕西,西安,710062 |
| |
| 基金项目： | 国家自然科学基金资助项目(10271069)，陕西师范大学博士创新基金资助项目 |
| |
| 摘 要： | 对于CONT的任意一个笛卡儿闭的满子范畴C,构造CONT的两个新的满子范畴R-C(以C对象的收缩为对象的范畴)和B-C(以C扩张序列的双极限为对象的范畴),并证明了它们都是笛卡儿闭范畴。由于R-C和B-C都包含C为其满子范畴,利用上述结果可得CONT的极大笛卡儿闭子范畴必对收缩和双极限封闭。本文还从范畴笛卡儿闭性的角度给出了Domain理论中一个公开问题的等价描述。
|
| 关 键 词： | 连续domain Scott连续映射 收缩 双极限 笛卡儿闭范畴 |
| 文章编号： | 1001-7402（2006）06-0028-07 |
| 收稿时间： | 2005-10-28 |
| 修稿时间： | 2005年10月28 |
Two Important Properties of Cartesian Closed Domain Categories |
| |
| LIU Ni.Two Important Properties of Cartesian Closed Domain Categories[J].Fuzzy Systems and Mathematics,2006,20(6):28-34. |
| |
| Authors: | LIU Ni |
| |
| Abstract: | For every Cartesian closed full subcategory WTHT]C of CONT, the induced categories R-WTHT]C (the category of all retracts of WTHT]C-objects and Scott continuous) and B-WTHT]C (the category of all bilimits of WTHT]C-expanding-sequences and Scott continuous) are both proved to be Cartesian closed full subcategories of CONT. Since R-WTHT]C and B-WTHT]C both contain WTHT]C as their full subcategory, a maximal Cartesian closed full subcategory of CONT must be closed with both retracts and bilimits of expanding- sequences. Also an equivalent statement of the famous open question in domain theory is given in terms of Cartesian closedness. |
| |
| Keywords: | Continuous Domain Scott Continuous Mapping Retract Bilimits Cartesian Closed Category |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
