The Maximum Modulus Principle

We prove the maximum modulus principle from complex analysis! (more advanced material, approx second year mathematics undergraduate)

Statement

No Diffeomorphism Between R^n and R^m

As I am learning about manifold theory, I thought I’d share a neat and short proof that R^n and R^m aren’t diffeomorphic. This means there is no continuous, bijective and infinitely differentiable function from R^n to R^m whose inverse is also bijective and…