User blog comment:Rgetar/Proof that limit of epsilon numbers is epsilon number/@comment-35470197-20200103082818/@comment-35470197-20200103123914

Good! The same computation holds even if you consider two or more Scott continuous functions (e.g. φ(n,-) for all n < ω). That is why the enumeration of (not necessarily single) Scott continuous functions (e,g, φ(ω,-)) is again Scott continuous.