FS-domains are not always RB-domains

2026/07/01 by Yuxu Chen, Hui Kou, Zhenchao Lyu · 1 voice
Mathematics · #math.GN

paper · pdf

arxiv published 2026/07/01 · arxiv updated 2026/07/04

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.

Citations

• Convex optimization
• A type-theoretical alternative to ISWIM, CUCH, OWHY

Discussions

• Yuxu Chen, Hui Kou, Zhenchao Lyu: FS-domains are not always RB-domains https://arxiv.org/abs/2607.00568 https://arxiv.org/pdf/2607.00568 https://arxiv.org/html/2607.00568 [bsky, 0 points, 0 comments]

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