%0 Journal Article %T A note on the problem when FS-domains coincide with RB-domains %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Zou, Zhiwei %A Li, Qingguo %A Guo, Lankun %D 2018 %\ 01/01/2018 %V 8 %N 1 %P 51-59 %! A note on the problem when FS-domains coincide with RB-domains %K FS-domains %K RB-domains %K Super finitely separating functions %K L-domains %R 10.29252/cgasa.8.1.51 %X In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilattice is an FS-domain if and only if it is an RB-domain; an L-domain is an FS-domain if and only if it is an RB-domain. These results are expected to provide useful hints to the open problem of whether FS-domains are identical with RB-domains. %U https://cgasa.sbu.ac.ir/article_47217_df93e16f640375823b7ff13404710dde.pdf