On relatively normal spaces, relatively regular spaces, and on relative property (a)

被引：11
|
作者：
Matveev, MV
Pavlov, OI
Tartir, JK
机构：
[1] Moscow NE Bauman State Tech Univ, Moscow 107005, Russia
[2] Ohio Univ, Dept Math, Athens, OH 45701 USA
来源：
TOPOLOGY AND ITS APPLICATIONS | 1999年 / 93卷 / 02期
关键词：
relative topological property; normal; regular; almost compact; (a)-space; acc-space; a-star-Lindelof space;
D O I：
10.1016/S0166-8641(97)00265-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Spaces which have a certain relative topological property in every larger space from a certain class are investigated. It is proved that a regular (Tychonoff) space Y is normal in every larger regular (Tychonoff) space if and only if Y is Lindelof or normal almost compact. A functionally Hausdorff space Y is regular in every larger functionally Hausdorff space if and only if Y is compact. A Hausdorff (regular, Tychonoff) space Y is relatively (a) in every larger Hausdorff (regular, Tychonoff) X if and only if Y is compact. (C) 1999 Elsevier Science B.V. All rights reserved.
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页码：121 / 129
页数：9
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