Domains via approximation operators.
In this paper , we tailor-made new approximation operators specially suited for domain theory. Our approximation operators offers a fresh perspective to existing concepts and results in domain theory, but also reveals 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) we discussed the property which named one-step closure. 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.
Publisher URL: http://arxiv.org/abs/1607.01164
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