关于Priestley空间的超空间的注记
Remarks on Hyperspaces for Priestley Spaces
摘要：
Stone空间的Vietoris空间在模态逻辑的共代数方法中起着重要的作用。当将其推广到正模态逻辑时，存在基于Priestley空间上的各种拓扑的各种相关的超空间构造以及将闭集的超空间拓扑化的机制。一些作者考虑了Priestley空间的超空间及其在正模态逻辑的共代数方法中的应用。混合的技术从范畴论，点自由拓扑，和Priestley对偶已被采用。我们的目标是提供一个统一的方法，这一领域的研究只依赖于一个基本的熟悉Priestley对偶和相关的免费建设的分配格。
英文摘要：
The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of relevant hyperspace constructions based on various topologies on a Priestley space and mechanisms to topologize the hyperspace of closed sets. A number of authors considered hyperspaces of Priestley spaces and their application to the coalgebraic approach to positive modal logic. A mixture of techniques from category theory, pointfree topology, and Priestley duality have been employed. Our aim is to provide a unifying approach to this area of research relying only on a basic familiarity with Priestley duality and related free constructions of distributive lattices.
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