在Quantale中讨论了与Gabriel拓扑密切关联的闭滤子,给出了闭滤子与闭映射之间的相互确定关系.证明了凝聚左侧Quantale Q的闭滤子全体F(Q)在包含序下构成Frame,并且Q的紧闭滤子全体Fc(Q)是F(Q)的子Frame.最后,证明了凝聚双侧交换Quantale的紧闭滤子全体在包含序下构成Coherent Frame.
In this paper, we discuss the relationships between closed maps and closed filters which is closely related with Gabriel topologies. It is proved that the set of all closed filters F(Q) on a coherent left-sided quantale ordered under inclusion is a frame and the set of all compact closed filters Fc(Q) is asubframe of F(Q). It is given that the set of all closed filters'on a coherent two-sided commutative quantale ordered under inclusion is a coherent frame.