2022/04/20 by Xiaoquan Xu, Xu, Xiaoquan
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2204.09512
In this paper, for a full subcategory K of the category of all T0 spaces with continuous mappings, we investigate the questions under what conditions the K-reflection of a Scott space is still a Scott space and under what conditions the Scott K-completion of a poset exists. Some necessary and sufficient conditions for the K-reflection of a Scott space to be a Scott space and for the existence of Scott K-completion of a poset are established, respectively. It is shown that neither the sobrification nor the well-filtered reflection of the Johnstone space is a Scott space. The K-reflections of Alexandroff spaces and the K-completions of posets are also discussed.