I wonder if someone could provide me a proof (or indicate me where to find it )to the following problem:
Let C be a seccionally differentiable Jordan curve and f a diffeomorphism taking an open set that contains C onto an open set. Suppose the winding number
of C with respect to a point of the interior of C is 1. Prove that if the jacobian of f is positive, the winding number of f(C) with respect to a point of the interior of f(C) is 1.
Note. One can use if necessary Greenīs Theorem, where positive orientation of a Jordan curve means that his winding number with respect to a point of its
interior is 1. The proof I am seeking must not involve homological algebra. I shall be very much grateful to whom kindly help me. paulo1941