k-有界清醒的不存在性
Nonexistence of k-bounded sobrification
摘要：
本文主要研究k-有界sobrification空间，证明了不允许任何k-有界sobrification的T_0空间X的存在性。这加强了Zhao，Lu和Wang的结果，他们证明了标准k-有界sobrification不存在。我们的工作给出了Zhao和Ho的一个问题的完整解，并证明了与Sob和BSob不同，所有k-有界sober空间的范畴KBSob不是所有T_0空间的范畴Top_0的反射子范畴.进一步，我们引入了qk-有界sober空间的概念，证明了范畴KBSob是所有qk-有界sober空间和保既有不可约上确界的连续映射的范畴QKBSob的全反射子范畴.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
