caa a22 4500 60546216X CHVBK 20210128100246.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10114-015-3676-z doi (NATIONALLICENCE)springer-10.1007/s10114-015-3676-z QFS-domains and quasicontinuous domains [Elektronische Daten] [Wen Zhang, Xiao 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 QFS-domains; (3) for a quasicontinuous domain L, L is Lawson compact iff L is a finitely generated upper set and for any x 1, x 2 ∈ L and finite G 1, G 2 ⊆ L with G 1 ≪ x 1, G 2 ≪ x 2, there is a finite subset F ⊆ L such that ↑ x 1∩ ↑ x 2 ⊆↑ F ⊆↑ G 1∩ ↑ G 2; (4) L is a QFS-domain iff L is a quasicontinuous domain and given any finitely many pairs {(F i , x i ): F i is finite, x i ∈ L with F i ≪ x i , 1 ≤ i ≤ n}, there is a quasi-finitely separating function δ on L such that F i ≪ δ(x i ) ≪ x i . Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 QFS-domain nationallicence quasicontinuous domain nationallicence Scott topology nationallicence Lawson compact nationallicence Zhang Wen Department of Mathematics, Sichuan University, 610064, Chengdu, P. R. China aut Xu Xiao Department of Mathematics, Jiangxi Normal University, 330022, Nanchang, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 295-304 1439-8516 31:2<295 2015 31 10114 https://doi.org/10.1007/s10114-015-3676-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-3676-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Wen Department of Mathematics, Sichuan University, 610064, Chengdu, P. R. China aut NATIONALLICENCE 700 1- Xu Xiao Department of Mathematics, Jiangxi Normal University, 330022, Nanchang, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 295-304 1439-8516 31:2<295 2015 31 10114