A note on D-spaces and infinite unions

被引：14

作者：

Peng, Liang-Xue ^{[1
]}

机构：

[1] Beijing Polytech Univ, Coll Appl Sci, Beijing 100022, Peoples R China

来源：

TOPOLOGY AND ITS APPLICATIONS | 2007年 / 154卷 / 11期

关键词：

D-space; k-network; sequential space; compact;

D O I：

10.1016/j.topol.2007.01.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that if X is a countably compact space that is the union of a countable family of D-spaces, then X is compact. This gives a positive answer to Arhangel'skii's problem [A.V. Arhangel'skii, D-spaces and finite unions, Proc. Amer. Math. Soc. 132 (7) (2004) 2163-2170]. In this note, we also obtain a result that if a regular space X is sequential and has a point-countable k-network, then X is a D-space. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：2223 / 2227

页数：5

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