Topological Structure And Category Properties Of Complete Directional Complete Sequences

In this thesis, we mainly investigate three sections as follows:The first part of this article, first of all, discuss the relationship between the Scott topology on product of cdcpos and the product of Scott topologies. Then we discuss some basic properties of the way-below relation of Scott continuous functions on cdcpos.In the second part, we firstly discuss the completeness of the cat-egory of cdcpos and the existence of its co-product. Then, we prove its subcategory L-CDCPO is not complete, and give a complete sub-category of L-CDCPO, also, it is proved that the co-product of the subcategory exists.In the third part, we firstly discuss some properties of the Bi-Z-Scott topology. Also it is proved that the image of Bi-Z-domain under Bi-Z-Scott continuous maps which preserves the <<Z and pz relation are still Bi-Z-domains.