Definition:Compatible Charts/Smooth

Definition
Let $M$ be a topological space.

Let $d$ be a natural number.

Let $\struct {U, \phi}$ and $\struct {V, \psi}$ be $d$-dimensional charts of $M$.

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

is of class $C^\infty$.