 The tensor product as the map formula_226 is also continuous, where formula_227 is the Schwartz space of rapidly decreasing functions.These maps induce canonical surjective TVS-isomorphisms 
formula_228 
and 
formula_229, 
where formula_230 represents the completion of the injective tensor product (which in this case is identical to the completion of the projective tensor product, since these spaces are nuclear).Furthermore, there are canonical TVS-isomorphisms 
formula_231 
and 
formula_232.