论文标题
K结合的Sobrification不存在
Nonexistence of k-bounded sobrification
论文作者
论文摘要
在本文中，我们将重点关注k结合的清醒空间，并显示T_0空间X的存在不承认任何K结合的Sobrification。这加强了Zhao，Lu和Wang的结果，他们证明了规范的K结合的Sobrification不存在。我们的工作为Zhao和Ho问题提供了完整的解决方案，并表明与SOB和BSOB不同，所有K结合的清醒空间的类别KBSOB并不是所有T_0空间中TOP_0的反思性子类别。此外，我们介绍了QK结合的清醒空间的概念，并证明了类别KBSOB是所有QK-KBSOB类别的完整反思性子类别，这些类别是所有QK结合的清醒空间的QKBSOB，并且可以保留现有的不可避免的Suprema。
In this paper, we will focus on k-bounded sober spaces and show the existence of a T_0 space X not admitting any k-bounded sobrification. This strengthens a result of Zhao, Lu and Wang, who proved that the canonical k-bounded sobrification does not exist. Our work provides a complete solution to a question of Zhao and Ho, and shows that unlike Sob and BSob,the category KBSob of all k-bounded sober spaces is not a reflective subcategory of the category Top_0 of all T_0 spaces. Furthermore, we introduce the notion of qk-bounded sober spaces and prove that the category KBSob is a full reflective subcategory of the category QKBSob of all qk-bounded sober spaces and continuous mappings preserving existing irreducible suprema.
