发表机构
ITAM, Instituto Tecnológico Autónomo de México; New Mexico State University; CECAT, Chapman University（墨西哥自治理工学院; 新墨西哥州立大学; 查普曼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出完全正则性作为完全正规性的弱化，通过多种刻画并引入完全正则化构造，论证其重要性不亚于Isbell布尔化。
AI 中文摘要
我们引入完全正则性的概念，作为空间和locale中完全正规性的适当弱化。我们利用Dedekind-MacNeille完备化、内射包和子locale给出了多种刻画。我们将新的完全正则框架类置于多种已被充分研究的框架类之中。我们还引入了完全正则框架的完全正则化构造，将其与Isbell著名的布尔化构造进行比较，并论证其至少与后者同等重要。
英文摘要
We introduce the notion of perfect regularity as an appropriate weakening of perfect normality, both for spaces and locales. Various characterizations are given, using Dedekind-MacNeille completions, injective hulls, and sublocales. We place the new class of perfectly regular frames among various well-studied classes of frames. We also introduce the construction of perfect regularization of a completely regular frame, compare it to Isbell's well-known booleanization construction, and argue that it is at least as important as the latter.
