论文标题
连续晶格的谓语理论
Predicative theories of continuous lattices
论文作者
论文摘要
我们介绍了一个强大的接近联接 - 间 - 米拉门宫的概念，这是一个连续晶格的谓词概念，它是代数晶格类别的karoubi封底。在更广泛的接近posets（也称为抽象基础或R结构）上，强大的近距离联接 - 隔离式可以以较低的PowerLocale的煤层为特征。此外，在接近POSETS类别上，双重电磁界的山地上，可以通过强大的接近联接 - 隔离来表征局部紧凑的地区。我们还提供了强大的近距离联接 - 隔离的更合乎逻辑的表征，称为强烈的连续封面，该封面使用构成关系来展示基本的联接 - 偏 - 米拉门。我们表明，这种结构自然对应于无谓词无点拓扑中连续晶格的概念。我们的结果使得无点拓扑的连续晶格概念的谓语和细微方面更加明确。
We introduce a notion of strong proximity join-semilattice, a predicative notion of continuous lattice which arises as the Karoubi envelop of the category of algebraic lattices. Strong proximity join-semilattices can be characterised by the coalgebras of the lower powerlocale on the wider category of proximity posets (also known as abstract bases or R-structures). Moreover, locally compact locales can be characterised in terms of strong proximity join-semilattices by the coalgebras of the double powerlocale on the category of proximity posets. We also provide more logical characterisation of a strong proximity join-semilattice, called a strong continuous finitary cover, which uses an entailment relation to present the underlying join-semilattice. We show that this structure naturally corresponds to the notion of continuous lattice in the predicative point-free topology. Our result makes the predicative and finitary aspect of the notion of continuous lattice in point-free topology more explicit.
