一句话：引入受粗糙集启发的近似算子，为 Domain 理论中的连续性、way-below 关系与 Scott 拓扑提供新刻画。
本文为 Domain 理论量身设计了一类受粗糙集理论启发的近似算子。这些算子既能以新视角解释已有概念与结果，也能导出新的 Domain 理论结论。具体而言，连续偏序集上 way-below 关系的著名插值性质等价于某集合算子的幂等性；偏序集的连续性可由 Scott 闭包算子与由 way-below 关系诱导的上近似算子重合来刻画；meet-continuity 可由拓扑闭包算子的某性质建立。作者还证明，对每个近似关系可定义相容的序拓扑，且在连续偏序集情形，way-below 关系对应的拓扑恰为 Scott 拓扑，并对该新拓扑做了初步研究。
In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal ways to establishing novel domain-theoretic results. For instance, (1) the well-known interpolation property of the way-below relation on a continuous poset is equivalent to the idempotence of a certain set-operator; (2) the continuity of a poset can be characterized by the coincidence of the Scott closure operator and the upper approximation operator induced by the way below relation; (3) meet-continuity can be established from a certain property of the topological closure operator. Additionally, we show how, to each approximating relation, an associated order-compatible topology can be defined in such a way that for the case of a continuous poset the topology associated to the way-below relation is exactly the Scott topology. A preliminary investigation is carried out on this new topology.Comment: 17 pages; 1figure, Domains XII Workshop