\begin{definition}[Definition:Compatible Charts/Smooth]
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''' {{iff}} their transition mapping:
:$\psi \circ \phi^{-1} : \map \phi {U \cap V} \to \map \psi {U \cap V}$
is of class $C^\infty$.
Category:Definitions/Manifolds
\end{definition}