Partial Agreement Complete Posets And α ~ * (M) - Bi-continuous Posets

This thesis contains three chapters, and the main contents are as follows:In the first chapter, we introduce some basic knowledge related to this thesis, including the Scott topology and the convergence of limit, etc.In the second chapter, we mainly investigate the following four aspects:Firstly, we compare the directed posets with uniformed posets on concepts and properties, and then we give some examples to explain the relations and differences between them.Secondly, we discuss some properties of uniformed Scott continu-ous on posets; and then, we prove some interesting conclusions.Thirdly, we give the concept of partially uniformed complete posets, and then discuss the relations and differences between partially uni-formed complete posets and partially directed-complete posets.Finally, we introduce the concepts of pre-uniformed Scott topology and discuss its properties.In the third chapter, we mainly investigate the following two as-pects:On the one hand, we introduce the concept of Lim-in f2conver-gence of nets and filters on posets, discuss the related properties, and prove the equivalence of net and its derived filter about Lim-in f2con-vergence, the equivalence of filter and its derived net about Lim-in f2convergence.On the other hand, we define the relation (?)α*(M) and the bicon-tinous of α*{M) on the basis of ordered convergence, and get some related properties.