Year: 2026
Type: preprint
Abstract: We prove that a domain $D$ is an RB-domain if and only if the function space $[D\to E]$ is continuous for every domain $E$, thereby resolving a conjecture of Luan and Li. More precisely, for each domain $D$ we construct an explicit algebraic test domain $A_D$ such that continuity of the single function space $[D\to A_D]$ already forces $D$ to be an RB-domain. For countably based domains $D$, the test domain can be chosen as a fixed domain that is independent of $D$. The analogous continuity characterization of FS-domains is false: the closed-disk domain is an FS-domain, but its function space into a suitable pointed algebraic domain is not continuous.
Source: arXiv (Cornell University)
Author: Chen, Yuxu
Institution: Sichuan University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213612184