Completion of quasi-uniform frames (Q1818918)

In the study of quasi-uniform frames there has been a division between those favoring covering quasi-uniformities and those preferring entourage quasi-uniformities. It seems to be emerging from the paper under review and [The Samuel compactification of a quasi-uniform frame, Topology Proc. 23 (to appear)] that both points of view are valuable. Using the entourage approach, the authors construct the unique completion of a quasi-uniform frame and show that a quasi-uniform frame \((L,{\mathcal U})\) is complete if, and only if, the uniform frame \((L,{\mathcal U}^*)\) is complete. In Proposition 3.5 the authors give a characterization of an entourage base for the quasi-uniformity of the completion, but in order to establish this characterization they make use of covering quasi-uniformities. It follows from their results that the category of complete quasi-uniform frames is a coreflective subcategory of the category of quasi-uniform frames.