In this paper, we answer two problems concerning sobriety. One concerns the existence of a closed set lattice whose Scott space is non-sober. Another is about the reflectivity of a category of k-bounded sober spaces. We also prove some sufficient conditions for the Scott space of a dcpo to be k-bounded well-filtered.

中文翻译：

---

关于拓扑空间清醒性的两个问题

在本文中，我们回答了两个与清醒有关的问题。一个问题涉及斯科特空间非清醒的封闭集合格的存在。另一个问题是关于k界清醒空间类别的反射率。我们还证明了足​​以对dcpo的Scott空间进行k界滤波的一些充分条件。