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 QFS- domains; （3） for a quasico...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 QFS- domains; （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 C L with G1 〈〈 x1, G2 〈〈 x2, there is a finite subset F C L such that ↑ x1 x2 G2; （4） L is a QFS-d0main 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 5 on L such that Fi 〈〈 δ（xi） 〈〈 xi.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.10861007,11161023)the Fund for the Author of National Excellent Doctoral Dissertation of China(Grant No.2007B14)+2 种基金the Ganpo 555 Programma for Leading Talents of Jiangxi Provincethe NFS of Jiangxi Province(Grant No.20114BAB201008)the Fund of Education Department of Jiangxi Province(Grant No.GJJ12657)
文摘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 QFS- domains; （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 C L with G1 〈〈 x1, G2 〈〈 x2, there is a finite subset F C L such that ↑ x1 x2 G2; （4） L is a QFS-d0main 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 5 on L such that Fi 〈〈 δ（xi） 〈〈 xi.
