Closure space has proven to be a useful tool to restructure lattices and various order structures.This paper aims to provide a novel approach to characterizing some important kinds of continuous domains by means of closure spaces. By introducing an additional map into a given closure space, the notion of F-augmented generalized closure space is presented. It is shown that F-augmented generalized closure spaces generate exactly continuous domains. Moreover, the notion of approximable mapping is identified to represent Scott-continuous functions between continuous domains. These results produce a category equivalent to that of continuous domains with Scottcontinuous functions. At the same time, two subclasses of F-augmented generalized closure spaces are considered which are representations of continuous L-domains and continuous bounded complete domains, respectively.
翻译:封闭空间已被证明是重组固定空间和各种秩序结构的有用工具。 本文旨在为通过封闭空间来描述一些重要的连续域提供一种新的方法。 通过在特定封闭空间中引入新的地图, 展示了F放大的通用封闭空间的概念; 显示F放大的普遍封闭空间产生完全连续的域。 此外, 类似的绘图概念被确定为代表连续域间Scott的连续功能。 这些结果产生了相当于连续功能的连续域的类别。 同时, F放大的普遍封闭空间分为两个亚类,分别代表连续的L域和连续的封闭完整域。