Cozero bases of frames

被引：27

作者：

Banaschewski, B

Gilmour, C ^{[1
]}

机构：

[1] Univ Cape Town, Dept Math & Appl Math, ZA-7701 Rondebosch, South Africa

[2] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2001年 / 157卷 / 01期

关键词：

D O I：

10.1016/S0022-4049(99)00167-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A. frame L which is generated by a regular sigma -frame (= cozero basis of L) is completely regular. Its cozero part CozL is then the largest cozero basis of L, and we characterize here those L for which it is the only such. Further, we give a similar characterization for the finitary analogue of this situation where regular sigma -frames are replaced by Boolean algebras. In addition, we consider the compactifications of a frame L provided by its cozero bases and show that all compactifications are of this kind iff L is pseudocompact. Finally, as an aside, we characterize the completely regular frames with unique compactification and their zero-dimensional counterparts. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: 54D35; 54D20; 54D60; 06E99.

引用

页码：1 / 22

页数：22

共 19 条

[1] COMPACTIFICATION AND LOCAL CONNECTEDNESS OF FRAMES [J].

BABOOLAL, D ;

BANASCHEWSKI, B .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1991, 70 (1-2) :3-16

[2] COMPACTIFICATION OF FRAMES [J].

BANASCHEWSKI, B .

MATHEMATISCHE NACHRICHTEN, 1990, 149 :105-116

[3]

BANASCHEWSKI B, 1984, J PURE APPL ALGEBRA, V33, P107, DOI 10.1016/0022-4049(84)90001-X

[4]

Banaschewski B., 1980, Houst. J. Math., V6, P301

[5]

Banaschewski B., 1989, CATEGORICAL TOPOLOGY, P257

[6]

BANASCHEWSKI B., 1996, Comment. Math. Univ. Carolin., V37, P577

[7]

Banaschewski B., 1997, TEXTOS MATEMATICA B, V12

[8]

Banaschewski Bernhard, 1993, Quaestiones Math., V16, P51

[9]

Gillman L., 1960, RINGS CONTINUOUS FUN

[10] REALCOMPACT SPACES AND REGULAR SIGMA-FRAMES [J].

GILMOUR, CRA .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1984, 96 (JUL) :73-79

← 1 2 →