2020/11/23 by Jing Lu, Kaiyun Wang, Lu, Jing +5
Medicine · Mathematics · Decision Sciences · #Intracranial Aneurysms: Treatment and Complications #Advanced Topology and Set Theory #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2011.11606
In this paper, we will focus on k-bounded sober spaces and show the existence of a T0 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 Top0 of all T0 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.