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.