A unified view of the Dedekind completion of pointfree function rings

We provide the appropriate unifying framework for the various descriptions of the Dedekind completion of the ring C( L ) of continuous real functions on a frame L . It is based on suitable Galois connections and a general result about Galois connections, showing once more the ubiquity of (Galois) adjunctions between partially ordered sets and their conceptual simplicity and effectiveness. Mathematics Subject Classification (2010) : Primary: 06D22; Secondary: 26A15, 54C30, 54D15. Keywords: Frame, locale, frame of reals, continuous real function, function ring, order complete, Dedekind completion, scale, normal semicontinuous real function, partial real function, Hausdorff continuous real function, cb-frame.