论文标题
概率电力域和准连续域
Probabilistic Powerdomains and Quasi-Continuous Domains
论文作者
论文摘要
$ x $上的概率powerdomain $ \ mathbf v x $是$ x $的所有连续估值的空间。我们表明，对于每个准连续域$ x $，$ \ Mathbf v x $再次是准连续域，Scott和弱拓扑再次同意$ \ Mathbf V x $。这也适用于$ x $的概率和亚概率估值的子空间。我们还表明，当$ x $不是准连续时，$ \ mathbf v x $上的Scott和弱拓扑可能会有所不同，并且我们提供了一个简单，紧凑的Hausdorff反例。
The probabilistic powerdomain $\mathbf V X$ on a space $X$ is the space of all continuous valuations on $X$. We show that, for every quasi-continuous domain $X$, $\mathbf V X$ is again a quasi-continuous domain, and that the Scott and weak topologies then agree on $\mathbf V X$. This also applies to the subspaces of probability and subprobability valuations on $X$. We also show that the Scott and weak topologies on the $\mathbf V X$ may differ when $X$ is not quasi-continuous, and we give a simple, compact Hausdorff counterexample.
