"The Scott topology is at least as fine as the relative topology." This is Corollary 7.3.2 in my book "Topology via Logic". "Are there conditions characterizing the coincidence of the two topologies on the points of a locale A?" I suspect that results such as Johnstone's "Scott is not always sober" might make exact characterizations difficult. Also, as stated in the original question, the characterization would have to include all locales without any points, so perhaps the class is not a terribly natural one to consider. Of course, a useful sufficient condition is for A to be completely distributive as a frame, this corresponding spatially to Scott topologies on continuous posets. (See Johnstone's "Stone Spaces".) Steve Vickers