Notes on Pointfree Disconnectivity with a Ring-theoretic Slant

被引：24

作者：

Dube, Themba ^{[1
]}

机构：

[1] Univ S Africa, Dept Math Sci, ZA-0003 Unisa, South Africa

来源：

APPLIED CATEGORICAL STRUCTURES | 2010年 / 18卷 / 01期

关键词：

Frame; F-frame; Basically disconnected; Extremally disconnected; Ring of continuous functions on a frame; Ring-ideal; Large compactification; F-RINGS;

D O I：

10.1007/s10485-008-9162-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give characterizations of extremally disconnected frames, basically disconnected frames and F-frames L in terms of ring-theoretic properties of the ring RL of continuous real-valued functions on L. Emanating from these are new (and purely ring-theoretic) proofs that a frame is extremally disconnected, basically disconnected or an F-frame iff the same holds for its Cech-Stone compactification.

引用

页码：55 / 72

页数：18

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