Let U⊂RnU \subset \mathbb R^nU⊂Rn be open. A function f:U→Rnf:\mathbb U \to \mathbb R^nf:U→Rn may be written as an mmm-tuple of functions fi:U→Rf_i:U\to \mathbb Rfi:U→R so that f=(f1,…,fm).f=(f_1,\dots,f_m).f=(f1,…,fm).