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The reflectivity of some categories of T0 spaces in domain theory
Citation
Shen, C., Xi, X., & Zhao, D. (2024). The reflectivity of some categories of T0 spaces in domain theory. Rocky Mountain Journal of Mathematics, 54(4), 1149-1166. https://doi.org/10.1216/rmj.2024.54.1149
Abstract
Keimel and Lawson (2009) proposed a set of conditions for proving the reflectivity of a category of topological spaces in the category of all T0 spaces. Recently, these conditions were used to prove the reflectivity of the category of all well-filtered spaces. We prove that, in certain sense, these conditions are not only sufficient but also necessary for a category of T0 spaces to be reflective. By applying this general result, we can easily deduce that several categories proposed in domain theory are not reflective, thereby answering a few open problems.
Publisher
Rocky Mountain Mathematics Consortium
Journal
Rocky Mountain Journal of Mathematics
DOI
10.1216/rmj.2024.54.1149