On dense subspaces of generalized ordered spaces

In this paper we study four properties related to the existence of a dense metrizable subspace of a generalized ordered (GO) space. Three of the properties are classical, and one is recent. We give new characterizations of GO-spaces that have dense metrizable subspaces, investigate which GO-spaces can embed in GO-spaces with one of the four properties, and provide examples showing the relationships between the four properties.