Proposition. (cpo)-continuous function space is a cpo [math-LVSY]

2023-12-10 · Lîm Tsú-thuàn

If DD and EE are cpo, then the continuous function space

[D→E]={f:D→E∣f is continuous} [D \to E] = \{ f : D \to E \mid f \ \text{is continuous} \}

is a cpo under the pointwise order.