 If the set formula_65 of continuous functions from formula_3 to formula_4 is given the compact-open topology, and if the space formula_4 is locally compact Hausdorff, then

is a homeomorphism.This is also the case when formula_3, formula_4 and formula_65 are compactly generated, although there are more cases.One useful corollary is that a function is continuous if and only if its curried form is continuous.