双Z-连续格和双Z-Scott拓扑的性质-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

双Z-连续格和双Z-Scott拓扑的性质

高嘉凌，赵彬*

(陕西师范大学数学与信息科学学院，陕西西安 710062)

高嘉凌, 男,硕士研究生,研究方向为格上拓扑与模糊推理.E-mail:sxsd2011@163.com.

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.

关键词：

双Z-Scott拓扑; 双Z-连续格; 双Z-Scott连续映射

收稿日期：

2011-03-16

中图分类号：

O153.1; O189.1

文献标识码：

文章编号：

1672-4291(2011)04-0006-04

基金项目：

国家自然科学基金资助项目(10871121).

Doi:

Properties of Bi-Z-Continuous lattices and Bi-Z-Scott topology

GAO Jia-ling, ZHAO Bin*

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

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.

KeyWords:

Bi-Z-Scott topology; Bi-Z-continuous lattices; Bi-Z-scott continuous maps