I-connected spaces and the images of metric spaces

被引：0
|
作者：
Ping, Zheng [1 ]
Liu, Fang [1 ]
Lin, Shou [2 ]
机构：
[1] Ningde Normal Univ, Dept Math, Ningde 352100, Fujian, Peoples R China
[2] Ningde Normal Univ, Inst Math, Ningde 352100, Fujian, Peoples R China
来源：
TOPOLOGY AND ITS APPLICATIONS | 2023年 / 326卷
关键词：
Ideal; T-convergence; T-connected set; T-csf-network; Metric space; T-covering mapping; T-sequential space; Quotient mapping; CONVERGENCE;
D O I：
10.1016/j.topol.2023.108414
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we discuss the following Tkachuk's question in the sense of ideal convergence [16,18]: Is any Tychonoff connected sequential space a quotient image of a connected metric space? It is proved that let I be an ideal on the set N then a topological space X is an I-connected space with an I-csf-network if and only if X is a continuous I-covering image of a connected metric space. It follows that a topological space X is a connected I-sequential space with an I-csf-network if and only if X is a quotient I-covering image of a connected metric space.(c) 2023 Elsevier B.V. All rights reserved.
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