相容连续偏序集上的ce-拓扑和cρ-拓扑

doi:10.6040/j.issn.1671-9352.0.2024.085

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (11): 153-158.doi: 10.6040/j.issn.1671-9352.0.2024.085

• • 上一篇

相容连续偏序集上的ce-拓扑和cρ-拓扑

郭智莲¹,杨海龙^2*

1.西北政法大学经济学院, 陕西西安 710063;2.陕西师范大学数学与统计学院, 陕西西安 710119

发布日期:2025-11-11
通讯作者: 杨海龙(1977— ),男,教授,博士生导师,博士,主要研究方向为智能信息处理与决策. E-mail:yanghailong@snnu.edu.cn
作者简介:郭智莲(1980— ),女,副教授,硕士生导师,博士,主要研究方向为格上拓扑与模糊推理. E-mail:gzl_434@163.com
基金资助:
国家自然科学基金资助项目(12171293);西北政法大学研究生教育教学改革研究项目(YJZC202312)

The ce-topology and cρ-topology on consistently continuous posets

GUO Zhilian¹, YANG Hailong^2*

1. College of Economics, Northwest University of Political Science and Law, Xian 710063, Shaanxi, China;
2. College of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China

Published:2025-11-11

摘要/Abstract

摘要： 在相容定向完备偏序集上引入ce-拓扑和cρ-拓扑的概念,给出在相容连续偏序集上的两类拓扑若干性质,证明相容连续偏序集上的基是cρ-拓扑的稠密集。

关键词: 相容连续偏序集, ce-拓扑, cρ-拓扑, 连续格

Abstract: The definitions of ce-topology and cρ-topology on consistently directedly complete posets are introduced. Some properties of them on consistently continuous posets are given. Furthermore, it is obtained that the basis on a consistently continuous partial order set is topologically dense.

Key words: consistently continuous posets, ce-topology, cρ-topology, continuous lattice

中图分类号:

O153.1

郭智莲,杨海龙. 相容连续偏序集上的ce-拓扑和cρ-拓扑[J]. 《山东大学学报(理学版)》, 2025, 60(11): 153-158.

GUO Zhilian, YANG Hailong. The ce-topology and cρ-topology on consistently continuous posets[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(11): 153-158.

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相容连续偏序集上的ce-拓扑和cρ-拓扑

The ce-topology and cρ-topology on consistently continuous posets

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