If , are connected open subsets of such that is simply connected, a differentiable map is a diffeomorphism if it is proper and if the differential is bijective (and hence a linear isomorphism) at each point in .
If  are connected open subsets of such that is simply connected a differentiable map is a diffeomorphism if it is proper and if the differential is bijective (and hence a linear isomorphism) at each point in 