 The Schwartz space is nuclear and the tensor product of two maps induces a canonical surjective TVS-isomorphisms 
formula_372, 
where formula_230 represents the completion of the injective tensor product (which in this case is the identical to the completion of the projective tensor product).The natural inclusion formula_374 is a continuous injection whose image is dense in its codomain, so the transpose formula_375 is also a continuous injection.Thus, the image of formula_309, denoted by formula_377, forms a space of distributions when it is endowed with the strong dual topology of formula_378 (transferred to it via the transpose map formula_379, so formula_313's topology is finer than the subspace topology that this set inherits from formula_46).