概率幂domain是人们为了考虑容纳概率计算的程序语言的指称语义数学模型而引入的。一个拓扑空间上的概率幂domain是指该拓扑空间上的所有特殊valuation的集合。申请人已经研究过底空间和它的概率幂构造之间的关系，证明了一个dcpo的概率幂domain是连续的蕴含原dcpo也是连续的。本项目拟综合运用序、拓扑和拓扑cone理论的方法来研究拓扑空间上的概率幂domain及其相关问题：（1）概率幂domain上的拓扑相关的问题；（2）寻找在概率幂构造下封闭的新结构。 对这些问题的研究不仅会推动Domain理论和拓扑学的进一步发展，而且在指称语义中也具有一定应用。

Probabilistic powerdomain is introduced for denotational semantic model of programming language with probabilistic feature. The probabilistic powerdomain of a topological space is defined as a set of all special valuations on the topological space.We have discussed some relationships between the underlying space and its probabilistic powerdomain and we show that a dcpo is continuous if its probabilistic powerdomain is continuous. In this project, we investigate some problems of probabilistic powerdomain by using methods from order theory,topology and topological cone theory: (1)The problems about the topology on probabilistic powerdomain. (2)To find some new structure which is closed under probabilistic powerdomain construction..By investigating these problems not only can improve the development of domain theory and topology, but also have some applications in denotational semantics.