双Z-连续格和双Z-Scott拓扑的性质

摘要

在完备格上定义了双Z-连续格和双Z-Scott拓扑,讨论了双Z-Scott拓扑的格序性质.得到了当P是Z-拟连续时,双Z-Scott拓扑是T2的;证明了双Z-连续格在保Z-双小于关系和对偶Z-双小于关系的双Z-Scott连续映射下的像仍是双Z-连续格.%Bi-Z-Continuous lattices and Bi-Z-Scott topology on complete lattices are introduced.Properties of Bi-Z-Scott topology are discussed.It is proved that Bi-Z-Scott topology is T2 when P is Z-quasicontinuous.Also it is proved that the image of Bi-Z-continuous lattices under Bi-Z-Scott continuous maps which preserves the z and z are still Bi-Z-continuous lattices.