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

@article{paperbot409,
  title = {Domains via approximation operators},
  author = {Zhiwei Zou and Qingguo Li and Weng Kin Ho},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 14, Issue 2},
  year = {2018},
  doi = {10.23638/lmcs-14(2:6)2018}
}