完全分配格上的极小族拓扑

采用极小族理论建立了完全分配格上的另外一种拓扑——极小族拓扑，使得最大标准极小族是该拓扑仅有的非平凡开集。给出了极小族拓扑的一些性质及该拓扑下函数连续的必要条件，讨论了该拓扑下映射的连续性和广义序同态的关系，证明了完全分配格上的标准极小族映射为广义序同态。
关 键 词 完全分配格; 极小族; 最大标准极小族; 极小族拓扑; 广义序同态

Abstract In this paper, a new topological space as well as minimal families topological space is established on completely distributive lattices by using the results of the minimal families, the result that the largest standard minimal families are only nontrivial open sets on this topology is proved .The properties and the sufficient and necessary condition for functional continuity on the minimal families topological space shall be given, the relation between the continuity and the generalized order homomorphism under the new topological space is discussed, the result that the standard minimal families mapping on completely distributive lattices is the generalized order homomorphism is obtained.
Key words completely distributive lattices; minimal families; the largest standard minimal families; minimal families topology