Some Properties Of Consistently Dcpo And Local Dcpo

In this paper,we mainly study some properties of consistently Dcpo and local Dcpo,then we promote the local Dcpo.By introducing the concept of LBF-Domain,we discuss some properties of the LBF-Domain.The main contents of this paper are as following:Chapter One: We introduce the background information of this paper,and expound the main contents and the important conclusions in this paper.Chapter Two: Some primary definitions,basic conclusions and properties of this paper are given.Chapter Three: Based on the concept of consistently Dcpo,we discuss some properties of consistently Dcpo and the relation between the mapping of consistently Dcpo and Galois connection,investigate some properties of mapping on consistently Dcpo.We give the definition of weak lower set operator,and then some basic properties are discussed.Finally,according to the definition of S-limit,some properties of S-limit in consistently Dcpo are researched,we also clarify the relationship among consistently Dcpo,consistently continuous domain and S-limit.Chapter Four: Based on the existing concept of local Dcpo and FS-Ldcpo,we define the LBF-Domain by combining finitely separability with local Dcpo,and study the relationship between the directed completions of FS-Ldcpo and FS-Domain.Lastly we research some properties of LBF-Domain and the reflective subcategory,Cartesian closed category of the category LBF-DOM.Chapter Five: We summarize the research results of this paper and give the prospects for possible research problems in the future.