The semicontinuous quasi-uniformity is known to be one of the most important examples of transitive quasi-uniformities. The aim of this paper is to show that various facts in classical topology connected with the semicontinuous quasi-uniformity and semicontinuous real functions may be easily extended to pointfree topology via a construction introduced by the authors in a previous paper. Several consequences are derived.

Keywords: frame, biframe, quasi-uniform frame, biframe of reals, semicontinuous real function, transitive quasi-uniformity, functorial quasi-uniformity, spectrum cover