regular continuous frame; perfect compactification
We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations is that the remainder of the regular continuous frame in each of its compactifications is compact and connected.
 Aarts, J. M., Boas, P. Van Emde: Continua as remainders in compact extensions
. Nieuw Arch. Wisk., III. Ser. 15 (1967), 34-37. MR 0214033
 Sklyarenko, E. G.: Some questions in the theory of bicompactifications
. Am. Math. Soc. Transl., II. Ser. 58 (1966), 216-244. DOI 10.1090/trans2/058/11