Given two domains, $D_1$, $D_2$, already equipped with Scott (or Lawson) topology, the product domain $D=D_1\times D_2$ has the Tychonoff product topology, e.g., Mathematical Theory of Domains, page 124.
I can't seem to find a similar discussion of the function space topology for $D=[D_1\rightarrow D_2]$, though I assume it's well-known. Can someone explain it and/or give a reference which discusses it?
More generally, if you have a general domain equation $D=F(D_1,\ldots,D_n)$, where $F(\cdot)$ is built up from $D_1,\ldots,D_n$ by usual operations like product and function space, what can you say about $D$'s Scott/Lawson topology? In particular, how can you construct the open sets of $D$ from the open sets of $D_1,\ldots,D_n$?