QFS-domains and Quasicontinuous Domains  

作　　者：Wen Feng ZHANG Xiao Quan XU 

机构地区：[1]Department of Mathematics, Sichuan University [2]School of Mathematics and Computer Science, Jiangxi Science & Technology Normal University [3]Department of Mathematics, Jiangxi Normal University

出　　处：《Acta Mathematica Sinica,English Series》2015年第2期295-304,共10页数学学报（英文版）

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);the Ganpo 555 Programma for Leading Talents of Jiangxi Province;the NFS of Jiangxi Province(Grant No.20114BAB201008);the Fund of Education Department of Jiangxi Province(Grant No.GJJ12657)

摘　　要：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.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.

关 键 词：QFS-domain quasicontinuous domain Scott topology Lawson compact 

分 类 号：O189[理学—数学]