Several Research Of Semi Continuous Dcpo And Pseudo Consistent Continuous Domain

Since the discovery of continuous lattices and algebraic lattices in 1970s, continuous lattice theory has been the active research field, and the extension is studied deeply. The concept of semi prime ideals was first put forward and enriched by Y. Ray. Wu Xiuhua gives a kind of new relation in the literature [3] by semi prime ideal, and some properties were applicatied to semi continuous lattices. The basic properties, characteristics of consistent continuous Domain, semi continuous dcpo concept can also be characterized similarly. In chapter three, the theory and ideals are given which about how to extend to extensive theory of continuous lattices. Domestic and foreign mathematicians' great interest has been attracted since D.S.Scott firstly introduces the Domain's concept, more research and lots of conclusions which are similar to those of continuous lattices are conducted at the same time. In chapter four and five, the concept and relative properties of pseudo consistently continuous Domain and its local base are introduced from the intrinsic characteristics with a broad perspective.This thesis mainly includes six parts:Chapter one:Introduction.We introduce the history and current situation of con-tinuous posets theory and category theory. Then a brief introduction to the launching of thesis work and some prior knowledge.Chapter two:Preliminary knowledge. In the chapter we define some notions and gives some theorems about continuous Domains we will use in this paper.Chapter three:In the chapter, we research theories of local semi-bases on semi-continuous dcpo. In this chapter, the internal relations and expanding method of relevant definitions and main properties are compared among the continuous lattice, semi continuous lattice semi continuous dcpo and strong semi continuous dcpo, and their relations and differences are obtained, so some supplements are made. As for the continuous posets, consistently continuous posets, weak Domain, exact Domain, some conclusion can also be obtained similarly.In the end, the concept of local semi base about semi continuous dcpo is introduced, then some relevant properties and conclusions are obtainedChapter four:In the chapter, according to the definition of consistent Domain, we give the definitions of pseudo consistent continuous Domain and the base of it, and then some properties and. equivalent characterizations are obtained, and lots of excellent properties and conclusion are also provided, so as to make a further extension to Domain theory. In the end, we introduce a kind of special consistent directed posets in pseudo consistent continuous poset.Chapter five:In the chapter,we research some properties of local base in pseudo consistent continuous Domain.Chapter six:As a kind of special elements, meet-irreducible element not only has some good properties, but also plays an important role in lattice theory. In this chapter,the property of meet-irreducible element is explored by introducing the concept of continuous meet-irreducible element.