In this paper, we show that(1) for each QFS-domain L, L is an ωQFS-domain iff L has a countable base for the Scott topology;(2) the Scott-continuous retracts of QFS-domains are QFSdomains;(3) for a quasicontinuous domain L, L is Lawson compact iff L is a finitely generated upper set and for any x1, x2 ∈ L and finite G1, G2■L with G1<
The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.
