In this paper, continuing the work of the first and third authors, we study the function spaces from coherent continuous domains to RB-domains. Firstly, we prove that the function spaces from coherent core compact spaces with compact open sets as a basis to bifinite domains (algebraic RB-domains) are algebraic. As an application, we give an example which shows that a function space from a coherent quasi-algebraic domain to a finite domain might not be coherent. Finally, we show that the function space from a coherent continuous domain to an RB-domain is an RB-domain. Particularly, a function space from an FS-domain (introduced by Achim Jung) to an RB-domain is an RB-domain. This addresses an old open problem of whether FS-domains are RB-domains.
Publication Source (Journal or Book title)
Topology and its Applications
Xi, X., Xu, L., & Lawson, J. (2016). Function spaces from coherent continuous domains to RB-domains. Topology and its Applications, 206, 148-157. https://doi.org/10.1016/j.topol.2016.04.001