AI 中文总结
本文针对Xu和Zhao提出的开放问题，证明了实直线上正则开集构成的完全布尔代数$\text{RO}(\bbR)$的Scott空间不是清醒的，给出该问题的否定答案。
AI 中文摘要
Xu和Zhao明确将实直线上正则开集构成的完全布尔代数$\text{RO}(\bbR)$的Scott空间是否为清醒的问题列为开放问题，后续综述也重申了该问题，本文给出该问题的否定答案。
英文摘要
Whether the Scott space of the complete Boolean algebra $\RO(\bbR)$ of regular open subsets in the real line is sober was explicitly recorded as an open problem by Xu and Zhao and was reiterated in a later survey. We give a negative answer to this problem in this paper.
