s2s2-Quasicontinuous posets

In this paper, we consider a common generalization of both s2s2-continuous posets and quasicontinuous domains, and we introduce new concepts of way below relations and s2s2-quasicontinuous posets. The main results are: (1) The way below relation on an s2s2-quasicontinuous poset has the interpolation property; (2) The λ2λ2-topology on an s2s2-quasicontinuous poset is completely regular; (3) A poset is s2s2-continuous iff it is meet s2s2-continuous and s2s2-quasicontinuous.