Lindelofness of lexicographic products of GO-spaces

被引：0
|
作者：
Mou, Lei [1 ]
Xu, Yanqin [1 ,2 ]
机构：
[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[2] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao 066004, Hebei, Peoples R China
来源：
TOPOLOGY AND ITS APPLICATIONS | 2022年 / 314卷
基金：
北京市自然科学基金;
关键词：
Lexicographic product; LOTS; GO-space; Lindelof;
D O I：
10.1016/j.topol.2022.108110
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider when a lexicographic product of GO-spaces is Lindelof. We mainly prove: (1) Let gamma be any ordinal. Assume that for each alpha < gamma, X-alpha is a Lindelof GO-space, and for each alpha >= 1, X-alpha has a minimum m(alpha) , and maximum M-alpha. Then the lexicographic product Pi X-alpha<gamma(alpha) of GO-spaces is also Lindelof. (2) Let gamma <= omega(1). Assume that for each alpha < gamma, X-alpha is a Lindelof subspace of an ordinal. Then the lexicographic product Pi(alpha<gamma) X-alpha , of GO-spaces is also Lindelof. (C) 2022 Elsevier B.V. All rights reserved.
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