In this paper, we mainly discuss some basic properties of Scott power spaces. For a $T_0$ space $X$, let $\mathsf{K}(X)$ be the poset of all nonempty compact saturated subsets of $X$ endowed with the Smyth order. It is proved that the Scott power space $Σ\mathsf{K}(X)$ of a well-filtered space $X$ is still well-filtered, and a $T_0$ space $Y$ is well-filtered iff $Σ\mathsf{K}(Y)$ is well-filtered and the upper Vietoris topology is coarser than the Scott topology on $\mathsf{K}(Y)$. A sober space is constructed for which its Scott power space is not sober. A few sufficient conditions are given under which a Scott power space is sober. Some other properties, such as local compactness, first-countability, Rudin property and well-filtered determinedness, of Smyth power spaces and Scott power spaces are also investigated.
Scott Function Spaces under One-Sided FS Assumptions: Counterexamples, Positive Results, and New Directions
School of Science, Beijing University of Post and Telecommunications（北京邮电大学理学院）；Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院数学与数学教育系）；School of Mathematics and Statistics, Yancheng Teachers University（盐城师范学院数学与统计学院）
School of Mathematics and Statistics, Guilin University of Technology, Guilin 541004, ChinaScott spaces of complete Boolean algebras need not be co-sober
School of Mathematics and Statistics, Guilin University of Technology（桂林理工大学数学与统计学院）；School of Mathematics and Statistics, Minnan Normal University（闽南师范大学数学与统计学院）
Probabilistic Powerdomains and Quasi-Continuous Domains
空间$X$上的概率幂域$\mathbf V X$是$X$上所有连续赋值的空间。我们表明，对于每一个准连续域$X$，$\mathbf V X$再次是一个准连续域，斯科特和弱拓扑，然后同意$\mathbf V X$。这也适用于$X$上的概率和子概率赋值的子空间。当$X$不是拟连续的时，$\mathbf V X$上的Scott拓扑和弱拓扑可能不同，并给出了一个简单的紧Hausdorff反例.
Sobriety of Regular Open Algebras in Second-Countable T3 Spaces
Yancheng Teachers University（盐城师范学院）；Beijing University of Posts and Telecommunications（北京邮电大学）；National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）
On three problems about well-filteredness of $T_0$-spaces
School of Mathematics and Statistics, Minnan Normal University（闽南师范大学数学与统计学院）；College of Mathematics and Information, Nanchang Hangkong University（南昌航空大学数学与信息学院）
