The monotone Lindelöf property and separability in ordered spaces

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