Definition:Compatible Charts/Smooth

Definition
Let $M$ be a topological space.

Let $d$ be a natural number.

Let $(U,\phi)$ $(V,\phi)$ be $d$-dimensional charts of $M$.

Then $(U,\phi)$ and $(V,\psi)$ are smoothly compatible their transition mapping:
 * $\psi \circ \phi^{-1} : \phi( U \cap V) \to \psi(U\cap V)$

is of class $C^\infty$.