闭元确定的拓扑系统中闭包元及其应用

doi:10.12263/DZXB.20210332

电子学报 ›› 2022, Vol. 50 ›› Issue (5): 1270-1276.DOI: 10.12263/DZXB.20210332

闭元确定的拓扑系统中闭包元及其应用

高雅, 吴洪博

陕西师范大学数学与统计学院，陕西西安 710062

收稿日期:2021-03-10 修回日期:2021-05-15 出版日期:2022-05-25
- 通讯作者:
- 吴洪博
- 作者简介:
- 高　雅　女， 1996年6月生于山西大同.现为陕西师范大学数学与统计学院硕士研究生.主要研究方向为非经典数理逻辑与格上拓扑.E-mail: 910653355@qq.com
  吴洪博　男， 1959年6月生于陕西咸阳.现为陕西师范大学数学与统计学院教授、博士生导师.主要研究方向为非经典数理逻辑与格上拓扑.E‑mail: wuhb@snnu.edu.cn
- 基金资助:
- 国家自然科学基金 (61572016)

Closure Elements in the Topological System Determined by Closed Elements with Applications

GAO Ya, WU Hong-bo

College of Mathematics and Statistics, Shaanxi Normal University, Xi'an, Shaanxi 710062, China

Received:2021-03-10 Revised:2021-05-15 Online:2022-05-25 Published:2022-06-18
- Corresponding author:
- WU Hong-bo
- Supported by:
- National Natural Science Foundation of China (61572016)

摘要/Abstract

摘要：

本文利用余Frame和点集两部分建立由闭元确定的拓扑系统，对其基本性质进行了讨论；通过闭元给出了点集部分的闭包元概念，并对闭包元性质进行了讨论. 在余Frame和点集部分之间利用双映射建立了闭包元算子，证明了与拓扑系统相关的Kuratovski闭包定理；作为应用，利用闭包元算子对闭元确定的拓扑系统之间的连续映射进行了等价刻画.

关键词: 拓扑系统, 余Frame, 闭元, 闭包元, 闭包算子, Kuratovski闭包定理, 连续映射

Abstract:

A topological system determined by closed elements is established with coframe and point set, and its basic properties are discussed. The concept of closure element of point set part is given through closed element, and the properties of closure element are discussed. The closed element operator is established through double mapping between coframe and point set, and the Kuratovski closure theorem related to topological system is proved. As an application, the continuous mapping between topological systems determined by closed elements is characterized by closure element operators.

Key words: topological system, coframe, closed element, closure element, closure operator, Kuratovski's closure theorem, continuous mapping

中图分类号:

O189.1

高雅, 吴洪博. 闭元确定的拓扑系统中闭包元及其应用[J]. 电子学报, 2022, 50(5): 1270-1276.

Ya GAO, Hong-bo WU . Closure Elements in the Topological System Determined by Closed Elements with Applications[J]. Acta Electronica Sinica, 2022, 50(5): 1270-1276.

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闭元确定的拓扑系统中闭包元及其应用

Closure Elements in the Topological System Determined by Closed Elements with Applications

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