Research On Several Properties Of QFS-Domain

In this thesis, we mainly investigate some characterizations of QFS-Domain and QFSposet. The content of this thesis are as fol-lowing:The first part of this thesis, first of all, we define the QFS-poset and discuss some basic properties of QFS-poset. Then we define some sums of QFS-posets, we show that QFS-posets are preserved by some sums of QFS-posets.In the second part, we firstly discuss the hereditability of QFS-Domain. Based on the subspaces of QFS-Domain, it is proved that QFS-Domains are hereditary for Scott closed sets and not hereditary for Scott open sets. We construct some particular Scott open sets, which are hereditary. Secondly, we discuss the completeness of cat-egory QFSDOM and the existence of co-product. Li Gaolin and Xu Luoshan proposed a question in the reference [8] that for any QFS-Domain P and Scott-continuous projection f on P, is f(P) always a QFS-Domains? We give an affirmative answer to this question under some additional conditions.In the third part, we first discuss the directed completions of QFS-posets. It is proved that every directed completion of QFS-posets is a QFS-Domain. Then, we discuss the categorical relationship be-tween QFSPOS and QFSDOM, and we show that QFSDOM is a full reflective sub category of QFSPOS.