On products of discretely generated spaces

被引：7

作者：

Murtinova, Eva ^{[1
]}

机构：

[1] Charles Univ, Fac Math & Phys, Dept Math Anal, Prague 18675 8, Czech Republic

来源：

TOPOLOGY AND ITS APPLICATIONS | 2006年 / 153卷 / 18期

关键词：

discretely generated; weakly discretely generated; strongly discretely generated;

D O I：

10.1016/j.topol.2005.11.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Assuming a measurable cardinal exists, we construct a pair of discretely generated spaces whose product fails to be weakly discretely generated. Under the Continuum Hypothesis, a similar result is obtained for a pair of countable Frechet spaces as well as for two compact discretely generated spaces whose product is not discretely generated. A somewhat weaker example is presented assuming Martin's Axiom for countable posets. Further, the class of strongly discretely generated compacta is shown to preserve discrete generability in products. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：3402 / 3408

页数：7