Wen Feng ZHANG, Xiao Quan XU
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 << x1, G2 << x2, there is a finite subset F ⊆ L such that ↑x1∩↑x2 ⊆↑F⊆↑ G1∩↑G2; (4) L is a QFS-domain iff L is a quasicontinuous domain and given any finitely many pairs {(Fi, xi) : Fi is finite, xi ∈ L with Fi << xi, 1 ≤ i ≤ n}, there is a quasi-finitely separating function δ on L such that Fi << δ(xi) << xi.