拓扑系统中开远域及其应用

doi:10.6040/j.issn.1671-9352.0.2018.532

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (11): 90-96.doi: 10.6040/j.issn.1671-9352.0.2018.532

拓扑系统中开远域及其应用

冯丹丹,吴洪博^*

陕西师范大学数学与信息科学学院, 陕西西安 710119

发布日期:2019-11-06
作者简介:冯丹丹(1992— ), 女, 硕士研究生, 研究方向为格上拓扑与非经典数理逻辑. E-mail:1990151738@qq.com*通信作者简介:吴洪博(1959— ), 男, 教授, 博士生导师, 研究方向为格上拓扑与非经典数理逻辑. E-mail:wuhb@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(61572016);国家自然科学基金资助项目(11531009)

Open remote neighborhoods of topological systems and their applications

FENG Dan-dan, WU Hong-bo^*

School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China

Published:2019-11-06

摘要/Abstract

摘要： 在拓扑系统中提出了点的开远域的概念并对其性质和应用进行了研究。首先,在拓扑系统中提出了点的开远域的概念,讨论了它的基本性质,并利用开远域系给出了确定拓扑系统的方法;其次,通过开远域系定义了拓扑系统之间的映射在给定点连续的定义,并由此给出了拓扑系统之间连续映射的等价刻画;最后,利用点的开远域系给出T0拓扑系统和T1拓扑系统的等价刻画。

关键词: 拓扑系统, 开远域, 开远域系, 连续映射, T0拓扑系统, T1拓扑系统

Abstract: The concept of open remote neighborhood is proposed in topological system, and its properties with applications are studied. At first, the concept of open remote neighborhood is proposed in topological system, and its basic properties are discussed. Furthermore, a method of determining topological system is given by open remote neighborhood systems. The definition of continuous of mapping at a fixed point between topological systems is defined by open remote neighborhood systems, by which the equivalent form of continuous mapping between topological systems is given. At last, the equivalent forms of some separations of topological systems are given by using the open remote neighborhood systems.

Key words: topological system, open remote neighborhood, open remote neighborhood system, continuous mapping, T0 topological system, T1 topological system

中图分类号:

O141.1

冯丹丹,吴洪博. 拓扑系统中开远域及其应用[J]. 《山东大学学报(理学版)》, 2019, 54(11): 90-96.

FENG Dan-dan, WU Hong-bo. Open remote neighborhoods of topological systems and their applications[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 90-96.

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拓扑系统中开远域及其应用

Open remote neighborhoods of topological systems and their applications

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