网收敛在刻画分离公理中的作用分析  

The Analysis of the Function of Net Convergence in Characterization of Separation Axiom

作　　者：田俊英 TIAN Junying(Changzhi Preschool Teachers College,Changzhi Shanxi 046400,China)

机构地区：[1]长治幼儿师范高等专科学校,山西长治046400

出　　处：《佳木斯大学学报（自然科学版）》2023年第6期174-176,共3页Journal of Jiamusi University：Natural Science Edition

摘　　要：序列收敛在拓扑学中有重要作用.在第一可数空间中,用序列收敛可以充分刻画其相关概念.但在一般拓扑空间中,需要网而不是序列作为基本收敛工具之一.本文意在探索网收敛在刻画低分离公理中的作用,同时,文中也尝试补充给出网对正则空间,正规空间的刻画.最后,肯定一个事实,拓扑与网收敛是等价的.Sequence convergence plays an important role in topology.In the first countable space,the related concepts can be fully characterized by sequence convergence.But in the general topological space,we need nets instead of sequences as one of the basic convergence tools.This paper aims to explore the role of net convergence in characterizing the axiom of low separation,and at the same time,it also tries to add the characterization of regular space and normal space of nets.Finally,we affirm the fact that topology is equivalent to network convergence.

关 键 词：拓扑空间 网收敛 分离公理 

分 类 号：O1[理学—数学]