Hassler Whitney's Hidden Treasure : Every Differentiable Manifold Can Be Made Smooth

Abstract: In this essay, we give background to differential topology and utilize approximation techniques to prove Hassler Whitney's classic result that a manifold with a $C^r$ differential structure, $r \geq 1$, admits a compatible $C^s$ differential structure, $r < s \leq \infty$. That is, every differentiable manifold is a smooth manifold.