We give a constructive account of the de Groot duality of stably compact spaces in the setting of strong proximity lattice, a point-free representation of a stably compact space. To this end, we introduce a notion of strong continuous entailment relation, which can be thought of as a presentation of a strong proximity lattice by generators and relations. The new notion allows us to identify de Groot duals of stably compact spaces by analysing the duals of their presentations. We carry out a number of constructions on strong proximity lattices using strong continuous entailment relations and study their de Groot duals. The examples include various powerlocales, patch topology, and the space of valuations. These examples illustrate the simplicity of our approach by which we can reason about the de Groot duality of stably compact spaces.

我们对强紧迫晶格设置中的稳定紧致空间的de Groot对偶性进行了建设性的解释，这是稳定紧致空间的无点表示。为此，我们引入了强连续蕴涵关系的概念，可以将其视为生成器和关系表示的强邻近晶格。新概念使我们能够通过分析表示形式的对偶来确定稳定空间的de Groot对偶。我们使用强连续蕴涵关系在强邻近格上进行了许多构造，并研究了它们的de Groot对偶。示例包括各种powerlocale，补丁拓扑和评估空间。这些例子说明了我们方法的简单性，通过它我们可以推断出稳定紧凑空间的de Groot对偶性。