Order Continuity of Locally Compact Boolean Algebras

被引：0
|
作者：
Xiao-Dong Zhang
Helmut H. Schaefer
Kasia Winkowska-Nowak
机构：
[1] Florida Atlantic University,Department of Mathematics
[2] Centrum Fizyki Teoretycznej Polska Akademia Nauk,undefined
来源：
Positivity | 1997年 / 1卷
关键词：
Boolean algebra; local compactness; measure algebra; ordercontinuity;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The main purpose of this paper is to exhibit the decisive role that order continuity plays in the structure of locally compact Boolean algebras as well as in that of atomic topological Boolean algebras. We prove that the following three conditions are equivalent for a topological Boolean algebra B: (1) B is compact; (2) B is locally compact, Boolean complete, order continuous; (3) B is Boolean complete, atomic and order continuous. Note that under the discrete topology any Boolean algebra is locally compact.
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页码：297 / 303
页数：6
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