Approximation Operators And Topologies On ?-continuous Posets And Weak Domains

Domain Theory was first proposed by Dana Scott in the late 1960s.It was original-ly designed to provide denotational semantics for functional programming languages.Now,Domain Theory has been closely related to other mathematical fields,for exam-ple-rough set theory.The relationship between Domain Theory and rough set theory is mainly embodied in two aspects:Domain Theory can be applied to rough set through formal concept analysis,and conversely the approximate operator in rough set can be used to study Domains.In this thesis,we study certain Domains with rough set method on existing results.The main contents include the following aspects:In Chapter 1,we mainly introduce the development history of Domain Theory,and briefly describe the creations of Domains and the meanings of studying Domains from two aspects.Then,the development of rough sets and the relationship between Domain Theory and rough sets are explored.additionally,the core contents and ideas of this thesis are put forward and some preliminary results needed for our discussion are given.In Chapter 2,We study the relationship between ?-continuous posets and ?-topology.We discuss the relationship between ?-topology and other topologies by using the upper and lower approximation operators defined by auxiliary relations.We also investigate the relationship between the upper and lower approximation operators and ?-closure and ?-interior.Finally,a new equivalent characterization of ?-continuous posets is displayed.In Chapter 3,We define a new upper and lower approximation operator with the weak way below relation on posets,and give equivalent characterizations for the wb-open sets and the wwb-open sets.We also investigate the relationshio among the wb-topology,wwb-topology and other topologies,and finally give the equivalent char-acterization for weak Domains.