SI-continuous spaces and continuous posets

Recently, Zhao and Ho introduced and studied SI-continuous spaces, which can be seen as topological counterparts of continuous posets. The main purpose of this paper is to investigate the relationships between SI-continuous spaces and continuous posets. We prove that a C-space is an SI-continuous space if and only if it is a continuous poset under the specialization order. Furthermore, we introduce the notion of strong SI-continuous spaces and construct an adjunction between the category of domains and the category of strong SI-continuous spaces.