Abstract
In domain theory, finitely separated (FS) domains occupy a central place as they form one of the maximal Cartesian Closed subcategories of pointed domains. It is well-known that algebraic FS are exactly the bifinite domains, and this immediately raises the question: Are FS-domains exactly the same thing as retracts of bifinite domains? Domains of this latter form are referred to as RB-domains. The guiding analogy comes from the classical fact that every continuous domain can be realized as a retract of an algebraic domain, suggesting that a similar correspondence might hold in the context of FS-domains. This talk provides an accessible introduction to the problem of whether FS = RB. I will review the definitions of FS-domains, bifinite domains, and RB-domains, illustrating each with examples. We will then trace the motivations behind the conjecture, survey the latest known results, and discuss why the problem has remained resistant to solution. While this problem may seem to be a boondoggle as the title suggests, I hope to articulate the technical challenges explicitly and encourage the building of new tools to bring it down. This talk is a belated spin-off from one of those many weekly discussions with Martín Escardó during my good old PhD days.
Talk Details
Speaker: Ho Weng Kin (Nanyang Technological University, Singapore)
Event: Types and Topology Workshop in Honour of Martin Escardo’s 60th Birthday
Date: Wednesday 17 December 2025
Time: 09:50 (recorded)
Slides: Available
Key Topics
- Domain theory
- Finitely separated (FS) domains
- Bifinite domains
- RB-domains (retracts of bifinite)
- Cartesian closed categories
- Continuous domains
- Algebraic domains
- Retraction theory
Personal Connection
This work stems from weekly discussions with Martín Escardó during the speaker’s PhD studies, highlighting the long-term influence of Escardó’s mentorship and collaborative approach to research.