Some Studies On Locally Continuous Domain Theory

Since 1970 s,domain theory was always being focused by computer science and mathematics.The objects of domain theory studying are the posets which satisfy some conditions and the mappings of them.And the research content is putting it onto more general ordered structure.The main work summed up in the following aspects:1.We deeply study locally continuous domains and its theory based on continuous domains.Firstly,we give the internal characterization on the base of the local neighborhood.Then some intrinsic characterizations of locally directed sets are introduced and we also get some equivalent characterizations about the base and weight on locally continuous domains.Finally,we study the relation of weight on the locally scott domain and(?).2.We propose the character and destiny on locally continuous domain.In the first place,we introduce the concepts of character and destiny based on the local base and the dense base.Next,the relations between the character and density on a locally continuous domain and that of the related topological space with locally Scott topology or locally Lawson topology are discussed.3.Based on the locally semicontinuous lattice,we define the locally semiprime base by using locally semiprime ideals.And we introduce some properties between the locally semiprime base and the left adjoint.4.We give the definition of locally consistent semicontinuous lattices.Based on locally consistent semiprime minimal subsets,we study the relationships among the locally consistent semicontinuous,preserving ?lc and locally consistent semiprime minimal subsets of mappings.