Abstract
Normality is a classical separation axiom in the context of topological spaces and frames (locales). We investigate it in the setting of biframes; the class of normal biframes includes the compact regular ones, the Lindelöf regular ones, the strictly zero-dimensional ones and the Boolean ones. We obtain an explicit description of the compact, regular coreflection of a normal, regular biframe, and conclude by proving a version of Urysohn's Lemma, which characterizes normal biframes in terms of maps from the real line.
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Schauerte, A. Normality for biframes. Appl Categor Struct 3, 1–9 (1995). https://doi.org/10.1007/BF00872946
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DOI: https://doi.org/10.1007/BF00872946