Map Class

A map u:R^n->R^n from a domain G is called a map of class C^r if each component of

u(x)=(u_1(x_1,...,x_n),...,u_m(x_1,...,x_n))

is of class C^r (0<=r<=infty or r=omega) in G, where C^d denotes a continuous function which is differentiable d times.