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

共 19 条

[1] CALIBERS OF COMPACT SPACES [J].

ARGYROS, S ;

TSARPALIAS, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 270 (01) :149-162

[2] BOOLEAN-ALGEBRAS WITHOUT FREE FAMILIES [J].

ARGYROS, S .

ALGEBRA UNIVERSALIS, 1982, 14 (02) :244-256

[3]

Comfort W.W., 1982, Cambridge Tracts in Mathematics, V79

[4] A MODEL IN WHICH GCH HOLDS AT SUCCESSORS BUT FAILS AT LIMITS [J].

CUMMINGS, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 329 (01) :1-39

[5]

Juhasz I., 1980, Mathematical Centre Tracts, V123

[6]

Juhasz I., 1984, HDB SET THEORETIC TO

[7]

Junqueira L.R., 2000, Topology Proc, V25, P225

[8] The topology of elementary submodels [J].

Junqueira, LR ;

Tall, FD .

TOPOLOGY AND ITS APPLICATIONS, 1998, 82 (1-3) :239-266

[9] Compact spaces, elementary submodels, and the countable chain condition [J].

Junqueira, Lucia R. ;

Larson, Paul ;

Tall, Franklin D. .

ANNALS OF PURE AND APPLIED LOGIC, 2006, 144 (1-3) :107-116

[10]

Koppelberg S., 1989, HDB BOOLEAN ALGEBRAS, V1

← 1 2 →