The monotone Lindelِf property and separability in ordered spaces

In this paper we investigate the relation between separability and the monotone Lindelِf property in generalized ordered (GO)-spaces. We examine which classical examples are or are not monotonically Lindelِf. Using a new technique for investigating open covers of GO-spaces, we show that any separable GO-space is hereditarily monotonically Lindelِf. Finally, we investigate the relation between the hereditarily monotonically Lindelِf property and the Souslin problem.