TY - JOUR ID - 47217 TI - A note on the problem when FS-domains coincide with RB-domains JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Zou, Zhiwei AU - Li, Qingguo AU - Guo, Lankun AD - College of Mathematics and Econometrics, Hunan University, Changsha, China AD - College of Mathematics and Computer Science, Hunan Normal University, Changsha, China Y1 - 2018 PY - 2018 VL - 8 IS - 1 SP - 51 EP - 59 KW - FS-domains KW - RB-domains KW - Super finitely separating functions KW - L-domains DO - 10.29252/cgasa.8.1.51 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_47217.html L1 - https://cgasa.sbu.ac.ir/article_47217_df93e16f640375823b7ff13404710dde.pdf ER -