Inverse functions for f:R^m-->R^m , or f:X^m-->Y^m Hi: This is , I guess a technical question: Given f:R^m --->R^m ; f=(f_1(x_1,..,x_m),....,f_m(x_1,...,x_m)) Then I guess f^-1 (of course, assume f is 1-1.). Is given by a "pointwise" inverse , (right?) i.e., f^-1 =(f_1^-1 (x_1,..,x_m) ,....,f_m^-1(x_1,..,x_m)) ?. Is there some theorem on existence of inverses if we only know f to be continuous ( I think there is no known test for whether a function into R^m is onto )? Thanks.