Compatibility Domain And Fuzzy Semi-continuous Continuous Domain Of

Domain theory is a foundation in the semantics of programming languages. The basic characteristics of domain theory is the close connection between order and topology, which makes it a study field of experts on both computer and mathematics in topology. Domain theory in close contact with many disciplines of Mathematics.In2000, the concept of consistently continuous domain is introduced by Pro-fessor Xu, which contains N and R the most commonly used. Many conceps and conclusions of continuous domains have been generalized in consistently continuous domain theory.In recent years, Zhang Dexue, Lai Hongliang and so on have studied the directed completion and continuity of fuzzy posets by Ω-categrical theory. Fan lei and Zhang Qiye etal stidy the quantitative Domain by fuzzy sets theory. Doctor Yao Wei have studied some import ant problems in fuzzy Domain theory in his doctoral thesis.Based on the above research, the thesis further expands consistently continuous domain theory and fuzzy Domain theory. The main contributions in this thesis are listed as follows:(1) The structures of consistently continuous domain are studied further.Some equivalent conditions of the base on consistently continuous poset are obtained. The concept of the weight on consistently continuous poset is introduced, and some relative relations between the weight of consistently continuous poset and that of the topological spaces with Scott topology are discussed. Some properties of the fixed point sets of stable mappings on consistently continuous L-domains and consistently commutating mappings on consistent FS-domains are discussed respectively.(2) The consistently semicontinuous domain and the topology on it are studied.We introducte the concept of prime ideal of posets, based of which, we give the concepts of semicontinuous domain and consistently semicontinuous domain. Further, the notions of consistently Quasi-semicontinuous domains and consistently Meet-semicontinuous domains are introduced, and equivalent characterizations of them are given. The relations of Quasi-semicontinuous domains, consistently Meet-semicontinuous domains and consistently semicontinuous domain are discussed. The consistently semi-Scott topology and consistently semi-Lawson topology on consis-tently continuous domains are given, and some relations of them are discussed. The continuous mappings of consistent μ-topology on consistently semi-continuous do-mains are constructed.(3)The properties of fuzzy semicontinuous domains and fuzzy strongly contin-uous domains are studied.Firstly, we introducte the concept of fuzzy prime ideal of fuzzy dcpo, and give the concept and properties of (?)Fc.Based of this, we give the notions of fuzzy semicontinuous domains and fuzzy strongly continuous domains. It is proved that fuzzy Dcpo L is fuzzy semicontinuous domains if and only if ((?)Fc,(?)) is a fuzzy galois between L and FCRd(L) and fuzzy Dcpo L is fuzzy strongly continuous domains if and only if ((?)Fc,(?)) is a surjective fuzzy galois between L and FCRd(L). We obtain the conclusion that fuzzy strongly continuous domains must be fuzzy semicontinuous domains and fuzzy continuous domains are fuzzy semicontinuous domains under certain conditions.(4) The properties of L-semi-Scott topology on fuzzy semicontinuous domains are studied.Firstly, the concept of L-semi-Scott topology on fuzzy semicontinuous domains are introduced, the equivalent characterizations of it are discussed, and a base of it is given. Secondly, some fuzzy continuous mappings are given, and the relations of them are discussed. Thirdly, we introduce the notion of L-semi-Scott open filter, and give the relation between L-semi-Scott open filter and fuzzy open filter. Last, the concept of L-semi-Scott convergence of L-Filter is given. It is proved that the fuzzy dcpos are fuzzy semi-continuous domains if and only if full layer L-Filter L-semi-Scott convergence to x is equivalent to convergencing to x on L-semi-Scott topology.