When does the class \([{\mathcal A} \longrightarrow {\mathcal B}]\) consist of continuous domains? (Q1873745)

The authors investigate the following problem: Given classes of domains (or topological spaces) \(A\) and \(B\), when are all function spaces \([A\to B]\) again continuous domains? The main result of this paper is that for \(A\) either all compact and core compact spaces or only the single domain consisting of a decreasing sequence with two lower bounds, then the largest \(B\) fulfilling the above condition consists of all continuous domains such that \(\downarrow x\) is a sub-semilattice for each \(x\). A similar result is given for \(L\)-domains.