NORMALITY FOR BIFRAMES

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 Lindelof 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.