 In the theory of function spaces, such as in functional analysis or homotopy theory, one is commonly interested in continuous functions between topological spaces.One writes formula_80 (the Hom functor) for the set of "all" functions from formula_3 to formula_4, and uses the notation formula_65 to denote the subset of continuous functions.Here, formula_84 is the bijection

while uncurrying is the inverse map.