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陕西师范大学学报（自然科学版）
数学与计算机科学
Quantale系统的空间化和Q-Locale化
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马娜娜， 赵彬*
（陕西师范大学 数学与信息科学学院， 陕西 西安 710062)
马娜娜，女，硕士研究生，研究方向为格上拓扑与模糊推理. E-mail:mmm.86@163.com.*通信作者： 赵彬，男，教授，博士研究生导师. E-mail:zhaobin@snnu.edu.cn.
摘要:
引入Quantale系统的概念,给出了Quantale系统的连续映射和同胚映射的定义,证明了同胚映射的逆仍为同胚映射.探讨Quantale系统的空间化和Q-Locale化,并在Quantale系统范畴和量子空间范畴之间建立伴随.证明了Quantale系统关于Quantale的Q-Locale是Quantale系统,Quantale系统的Q-Locale化是Q-Locale.建立了Quantale系统范畴和Q-Loc范畴之间的伴随.
关键词：
拓扑系统; Quantale系统; Q-Locale; 连续映射; 范畴
收稿日期：
2012-06-27
中图分类号：
O153.1
文献标识码：
A
文章编号：
1672-4291(2013)02-0009-05
基金项目：
国家自然科学基金资助项目(11171196）.
Doi:
The spatialization and Q-localification of a Quantale system
MA Na-na, ZHAO Bin*
(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
Abstract:
By introducing the concept of Quantale system, the continuous mapping and homeomorphism of Quantale systems are defined.It is proved that the inverse of a homeomorphism mapping is also a homeomorphism mapping. Then the spatialization and the Q-localification of a Quantale system are researched and the adjoint between the category of Quantale system and the category of quantum spaces is established.It is proved the Q-localification of a Quantale system and proved about Quantales is a Quantale system and the Q-localification of a Quantale system is Q-Locale. In the end, the adjoint between the category of Quantale systems and the category of Q-Loc is established.
KeyWords:
topological system; Quantale system; Q-Locale; continuous mapping; category

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