The semicontinuous quasi-uniformity of a frame, revisited

Abstract

In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Gutiérrez García, T. Kubiak and J. Picado [13]. Our purpose is to show how the basic facts about the semicontinuous quasi-uniformity can be nicely presented and proved with that tool at hand.