一句话：引入强邻近并半格作为直谓连续格概念，并用余代数与蕴含关系给出刻画。
论文研究如何在直谓（predicative）无点拓扑中刻画连续格。作者引入强邻近并半格（strong proximity join-semilattice），它可视为代数格范畴的 Karoubi 包络所导出的直谓连续格概念。文章用 proximity poset（抽象基/R-结构）上 lower powerlocale 与 double powerlocale 的余代数分别刻画强邻近并半格与局部紧 locales。进一步给出逻辑刻画：强连续有限覆盖，用蕴含关系表示底层并半格。结果表明该结构自然对应直谓无点拓扑中的连续格，并使连续格概念的直谓性与有限性特征更显式。
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.