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

GAO Ya; WU Hong-bo

doi:10.12263/DZXB.20210332

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

CORRESPONDENCE | 更新时间：2025-12-08

- Closure Elements in the Topological System Determined by Closed Elements with Applications
- ACTA ELECTRONICA SINICA Vol. 50, Issue 5, Pages: 1270-1276(2022)
- 作者机构：
  
  陕西师范大学数学与统计学院，陕西西安 710062
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20210332
  CLC： O189.1;O153.1;O141.1
- Received：10 March 2021，
  
  Revised：2021-05-15，
  
  Published：25 May 2022
- 稿件说明：
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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(05):1270-1276.

GAO Ya,WU Hong-bo.Closure Elements in the Topological System Determined by Closed Elements with Applications[J].ACTA ELECTRONICA SINICA,2022,50(05):1270-1276.
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(05):1270-1276. DOI： 10.12263/DZXB.20210332.

GAO Ya,WU Hong-bo.Closure Elements in the Topological System Determined by Closed Elements with Applications[J].ACTA ELECTRONICA SINICA,2022,50(05):1270-1276. DOI： 10.12263/DZXB.20210332.

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.

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.

关键词

Keywords

references

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