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 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 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.
Citation
Chong Shen. Xiaoyong Xi. Dongsheng Zhao. "THE REFLECTIVITY OF SOME CATEGORIES OF SPACES IN DOMAIN THEORY." Rocky Mountain J. Math. 54 (4) 1149 - 1166, August 2024. https://doi.org/10.1216/rmj.2024.54.1149
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