发表机构
School of Mathematics, Sichuan University（四川大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了域为RB-域等价于其到任意域的函数空间连续，并构造显式测试域，同时指出FS-域无类似刻画。
AI 中文摘要
我们证明一个域$D$是RB-域当且仅当对每个域$E$，函数空间$[D\ o E]$是连续的，从而解决了Luan和Li的一个猜想。更精确地，对每个域$D$，我们构造一个显式的代数测试域$A_D$，使得单个函数空间$[D\ o A_D]$的连续性已经迫使$D$成为RB-域。对于可数基域$D$，测试域可以选择为独立于$D$的固定域。FS-域的类似连续性刻画是错误的：闭圆盘域是FS-域，但其到适当的有指代数域的函数空间不是连续的。
英文摘要
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.
