Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces

In this paper i, n, m are elements of N. The following propositions are true: (1) Let f be a set. Then f is a partial function from Rm to Rn if and only if f is a partial function from 〈Em, ‖ · ‖〉 to 〈En, ‖ · ‖〉. (2) Let n, m be non empty elements of N, f be a partial function from Rm to Rn, g be a partial function from 〈Em, ‖·‖〉 to 〈En, ‖·‖〉, x be an element of Rm, and y be a point of 〈Em, ‖ · ‖〉. Suppose f = g and x = y. Then f is differentiable in x if and only if g is differentiable in y.