On embeddings of perfect GO-spaces into perfect LOTS (Q1375716)

The following questions, posed in [Problems in perfect ordered spaces, in `Open problems in topology' (1990; Zbl 0718.54001), 233-236] and [\textit{H. R. Bennett} and \textit{D. J. Lutzer} (eds.) Topology and order structures, Part 1, Math. Centre Tracts 142 (1981; Zbl 0453.00032)], remain unanswered: Does every perfect GO-space have a perfect orderable extension? Does every perfect GO-space have a perfect orderable extension in which it is embedded as a dense subspace? The authors give conditions under which these questions have affirmative answers and show by examples that the extensions they obtain need not have the requisite properties unless their conditions are met. Although the conditions are too involved to state here, it is reasonable to expect that they can readily be determined for a given GO-space.