FS-domains are not always RB-domains

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.