@article { author = {Zou, Zhiwei and Li, Qingguo and Guo, Lankun}, title = {A note on the problem when FS-domains coincide with RB-domains}, journal = {Categories and General Algebraic Structures with Applications}, volume = {8}, number = {1}, pages = {51-59}, year = {2018}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.8.1.51}, abstract = {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.}, keywords = {FS-domains,RB-domains,Super finitely separating functions,L-domains}, url = {https://cgasa.sbu.ac.ir/article_47217.html}, eprint = {https://cgasa.sbu.ac.ir/article_47217_df93e16f640375823b7ff13404710dde.pdf} }