A note on the problem when FS-domains coincide with RB-domains

Document Type: Research Paper


1 College of Mathematics and Econometrics, Hunan University, Changsha, China

2 College of Mathematics and Computer Science, Hunan Normal University, Changsha, China


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.


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