Quantale上的一致拓扑空间  

Uniform Topological Spaces on Quantales

作　　者：罗清君[1] 

机构地区：[1]西安财经学院统计学院,陕西西安710100

出　　处：《模糊系统与数学》2017年第1期35-38,共4页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目(61473336);陕西省自然科学基金项目(2014JQ1032);陕西省教育厅基金项目(16JK1302);西安财经学院基金项目(15JD01)

摘　　要：利用理想诱导的弱同余关系在Quantale上构造一致结构与一致拓扑,证明了所得的一致拓扑空间是不连通的、零维的、局部紧的、完全正则的第一可数空间,并且Quantale中的运算关于导出的一致拓扑是连续的。同时,给出了商拓扑的等价刻画。In the present paper, we establish first uniformities and uniform topologies on quantales by using the weak congruence induced by ideals. It is proved that these topological spaces are disconnected, zero-dimensional, locally compact, completely regular and first-countable spaces. Furthermore, operations on quantales are continuous with respect to the uniform topologies. Finally, the equivalent characterization of quotient topology on quotient algebras of quantales under the weak congruence induced by ideals is also given.

关 键 词：QUANTALE 理想 一致拓扑 

分 类 号：O153.1[理学—数学]