论文标题
提出商区域
Presenting quotient locales
论文作者
论文摘要
能够在其基础框架的介绍或等效地，与他们分类的几何理论相同的角度来处理地区通常是有用的。给定一个语言环境的演讲，可以通过简单地附加其他关系来获得其子宫群的演示文稿，但是商区域的情况更加微妙。我们提供了简单的程序，以获取来自父级场所介绍的开放人，适当的商或一般三构的演示。结果在Suplattice，Preatrame和DCPO覆盖范围定理的帮助下证明了结果，并应用于从真实和封闭单位间隔的圆圈中获得圆的演示。
It is often useful to be able to deal with locales in terms of presentations of their underlying frames, or equivalently, the geometric theories which they classify. Given a presentation for a locale, presentations for its sublocales can be obtained by simply appending additional relations, but the case of quotient locales is more subtle. We provide simple procedures for obtaining presentations of open quotients, proper quotients or general triquotients from presentations of the parent locale. The results are proved with the help of the suplattice, preframe and dcpo coverage theorems and applied to obtain presentations of the circle from ones for the reals and the closed unit interval.
