  The study of weak domains and quasicontinuous domains leads to the
consideration of two types generalizations of domains. In the current paper, we
define the weak way-below relation between two nonempty subsets of a poset and
quasiexact posets. We prove some connections among quasiexact posets,
quasicontinuous domains and weak domains. Furthermore, we introduce the weak
way-below finitely determined topology and study its links to Scott topology
and the weak way-below topology first considered by Mushburn. It is also proved
that a dcpo is a domain if it is quasiexact and moderately meet continuous with
the weak way-below relation weakly increasing.
