The cardinality of compact spaces satisfying the countable chain condition

被引：0

作者：

Usuba, Toshimichi ^{[1
]}

机构：

[1] Kobe Univ, Org Adv Sci & Technol, Nada Ku, Kobe, Hyogo 6578501, Japan

来源：

TOPOLOGY AND ITS APPLICATIONS | 2014年 / 174卷

关键词：

Compact space; Countable chain condition; Dyadic system; Elementary submodel space; Independent family; Precaliber;

D O I：

10.1016/j.topol.2014.05.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that for a compact Hausdorff space X, if lambda(c(X)) < w(X) for every infinite cardinal lambda < w(X) and lambda(c(X)) < cf(w(X)) for every infinite cardinal lambda < cf(w(X)), then Tikhonov cube (w(x))[0,1] is a continuous image of X, in particular the cardinality of X is just 2(w(X)). As an application of this result, we consider elementary submodel spaces and improve Tall's result in [17]. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：41 / 55

页数：15

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