Z_s-consistent Continuous Poset And Several Kinds Of Domains

Domain theory plays a fundamental semantics of programming languages. It is characterized by the close connection between order and topology, which makes it the common study field of both computer experts and mathematicians. Until now, some scholars have deeply researched the continuous domains, pseudocontinuous domains, sL-Domains, Z_S—consistent continuous posets and so on. On the base, some properties of bounded complete pseudocontinuous domains are discussed, the stable mapping between bounded complete pseudocontinuous domains are characterized ulteriorly. We have given the relation between algebraic subsL-Domain and projection pair, and a category character of Z_S—consistent continuous poset.Chapter one defines some notions and gives some theorems about continuous domains and category theory we will use in the paper.In Chapter 2, the free dcpo and free join-complete lattice generated by poset are given;the stongly free dcpo and strongly join-complete lattice are also given, we have discussed the conditions for them to be algebraic domains.In Chapter 3, we have discussed the pseudocontinuous domains and algebraicl sL-Domain. The products, quotients and subobjects of pseudocontinuous domains are given, and then some properties of bounded complete pseudocontinuous domains are given. We have characterized the stable mapping between bounded complete pseudocontinuous domains. We mainly discuss the relation between albebraic subsL- Domains and projection pair.In Chapter 4, We have discussed the Z_S—consistent poset system and a category characterization of it. The definition of Z_S—consistent continuou poset is inducted, then some properties of it are discussed. We mainly prove that the category of Z_S—consistent contiunous poset is dually equivalent to a full subcategory of the category of completely distributive lattices. Some other properties of Z_S-consistent continuous poset is also investigated.