AI 中文总结
本文通过子locale系统的闭包与内部算子重新表述适配locale与次适配locale的经典刻画，将相关概念拓展至更一般框架，得到通用结果、新性质并简化了经典证明。
AI 中文摘要
我们从子locale系统上的闭包算子与内部算子出发，重新表述适配locale与次适配locale的若干经典刻画。利用这些刻画，我们可将适配性与次适配性的概念拓展至更一般的框架。该方法不仅能得到更通用的结果，还能呈现适配性与次适配性的新性质，例如子locale补元的计算公式，同时也简化了若干经典结果的证明。
英文摘要
We start by rephrasing some well-known characterizations of fit and subfit locales in terms of closure and interior operators on the system of sublocales. Using these characterizations, we are able to extend the notions of fitness and subfitness to a more general setting. This approach not only allows us to obtain more general results, but also to present new properties of fitness and subfitness (such as a formula for the computation of supplements of sublocales). Using this approach we were also able to simplify the proofs of some well-known results.
Comments20 pages
