NOT ALL SIGMA-COMPLETE BOOLEAN-ALGEBRAS ARE QUOTIENTS OF COMPLETE BOOLEAN-ALGEBRAS

被引：5

作者：

DOW, A ^{[1
]}

VERMEER, J ^{[1
]}

机构：

[1] DELFT UNIV TECHNOL,DEPT MATH,DELFT,NETHERLANDS

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 116卷 / 04期

关键词：

(SIGMA-)COMPLETE BOOLEAN ALGEBRA; EXTREMALLY DISCONNECTED; BASICALLY DISCONNECTED;

D O I：

10.2307/2159505

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In Shelah's model of no Borel lifting of the measure algebra we show that there is a sigma-complete Boolean algebra of cardinality 2omega that is not a quotient of a complete Boolean algebra. By Stone duality, there is a basically disconnected space of weight 2omega that cannot be embedded into an extremally disconnected space.

引用

页码：1175 / 1177

页数：3

共 10 条

[1]

Balcar Bohuslav, 1989, HDB BOOLEAN ALGEBRAS, V3, P1239

[2]

DOW A, 1991, EXTREMALLY DISCONNEC

[3]

Hart K.P., 1990, OPEN PROBLEMS TOPOLO, P97

[4] HOMOMORPHIC IMAGES OF SIGMA-COMPLETE BOOLEAN ALGEBRAS [J].