Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58538120180101A note on the problem when FS-domains coincide with RB-domains51594721710.29252/cgasa.8.1.51ENZhiweiZouCollege of Mathematics and Econometrics, Hunan University, Changsha, ChinaQingguoLiCollege of Mathematics and Econometrics, Hunan University, Changsha, ChinaLankunGuoCollege of Mathematics and Computer
Science, Hunan Normal University, Changsha, ChinaJournal Article20161007In 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.http://cgasa.sbu.ac.ir/article_47217_df93e16f640375823b7ff13404710dde.pdf