A note on global implicit function theorems

Applying the theory of covering maps, we will give an extension of global implicit function theorems proved by Sandberg [1]. Although he mentioned the theory of covering maps, he did not appeal to it. In fact, under his assumptions we can prove that the projection map to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</tex> -coordinates becomes a covering map. Then, by the theory of covering maps, we can obtain more general results. In the case when the spaces are Euclidean spaces, we will give a sufficient condition for global solvability in terms of the derivatives.