Perfect GO-spaces which have a perfect linearly ordered extension (Q1372686)

The author considers the old problem of Bennett and Lutzer whether every perfect GO-space can be embedded in a perfect LOTS. In earlier work, in cooperation with \textit{T. Miwa} and \textit{Y.-Z. Gao} [Topology Appl. 66, 241-249 (1995; Zbl 0839.54024)], the author showed that there is an example of a perfect GO-space which cannot be embedded in a perfect LOTS as a dense subspace. A related problem is to characterize the perfect GO-spaces which admit an ``order preserving'' embedding in a perfect LOTS. In the present paper the author presents a characterization of such spaces in terms of the existence of a special \(\sigma\)-discrete subset.