论文标题
在斯科特电力空间
On Scott power spaces
论文作者
论文摘要
在本文中，我们主要讨论Scott Power Spaces的一些基本属性。对于$ t_0 $ space $ x $，令$ \ m rathsf {k}（x）$是所有非空的紧凑型饱和子集的poset，该子集的$ x $赋予了Smyth订单。 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）$。建造了一个清醒的空间，其Scott Power Space并非清醒。在Scott Power空间清醒的情况下给出了一些足够的条件。还研究了其他一些属性，例如局部紧凑性，首先算法，鲁丁特性和良好的滤波器确定性，对史密斯电力空间和斯科特电力空间进行了研究。
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.
