| 推理闭包空间的分离性 |
| |
| 引用本文： | 郭智莲,杨海龙,伏文清.推理闭包空间的分离性[J].西北大学学报,2012(1):12-16. |
| |
| 作者姓名： | 郭智莲 杨海龙 伏文清 |
| |
| 作者单位： | 陕西师范大学数学与信息科学学院;西北政法大学经济管理学院;西安工业大学理学院 |
| |
| 基金项目： | 国家自然科学基金资助项目(11171196);陕西省教育厅科学研究基金资助项目(11JK0484) |
| |
| 摘 要： | 目的引入推理闭包空间的T0,T1,T2,Sober以及Urysohn分离性,研究它们的若干性质。方法利用拓扑学中分离性的思想以及研究方法,讨论推理闭包空间的分离性。结果分别给出了它们的定义及相应的等价刻画,证明了T0,T1,T2及Urysohn分离性是可遗传的且在同胚映射下是保持拓扑不变的,得到了诸分离性之间的关系。结论通过推理闭包空间分离性的建立,展现和丰富了逻辑学的拓扑性质。
|
| 关 键 词： | 推理闭包空间 结论闭集 结论开集 分离性 |
Separation axioms in reasoning closure spaces |
| |
| GUO Zhi-lian,YANG Hai-long,FU Wen-qing.Separation axioms in reasoning closure spaces[J].Journal of Northwest University(Natural Science Edition),2012(1):12-16. |
| |
| Authors: | GUO Zhi-lian YANG Hai-long FU Wen-qing |
| |
| Institution: | 1.College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China; 2.School of Economics and Management,Northwest University of Politics and Law,Xi′an 710063,China; 3.College of Science,Xi′an Technological University,Xi′an 710032,China) |
| |
| Abstract: | Aim Separation axioms T0,T1,T2,Sober and Urysohn on reasoning spaces are given,and some properties of them are discussed.Methods Similar to the research methods of separation axioms on topological spaces,separation axioms on reasoning spaces are discussed.Results Firstly,the definitions and equivalent characterizations of T0,T1,T2,Sober and Urysohn are given.Secondly,it is proved that T0,T1,T2 and Urysohn are inherited and invariant under the homeomorphism.Lastly,the relations of them are given.Conclusion As the separation axioms T0,T1,T2,Sober and Urysohn on reasoning spaces are established,the topological properties of fuzzy logic is exploed and enriched. |
| |
| Keywords: | reasoning spaces conclusion closed sets conclusion open sets separation |
| 本文献已被 CNKI 等数据库收录！ |
|
