FS-domains are not always RB-domains

Yuxu Chen; Hui Kou; Zhenchao Lyu

FS-domains are not always RB-domains

General Topology 2026-07-01 v1

Authors: Yuxu Chen , Hui Kou , Zhenchao Lyu

Abstract

We prove that Lawson's planar closed-disk domain is not an RB-domain. This domain is the dcpo of all closed disks in the Euclidean plane, together with the whole plane as bottom, ordered by reverse inclusion. Since this domain is an FS-domain, it gives a concrete example of an FS-domain which is not an RB-domain, answering negatively the long-standing open problem in domain theory of whether FS-domains and RB-domains are identical.

Keywords

FS-domains RB-domains domain theory closed-disk domain dcpo

Cite

@article{arxiv.2607.00568,
  title  = {FS-domains are not always RB-domains},
  author = {Yuxu Chen and Hui Kou and Zhenchao Lyu},
  journal= {arXiv preprint arXiv:2607.00568},
  year   = {2026}
}