\begin{definition}[Definition:Compatible Atlases/Definition 1]
Let $M$ be a topological space.
Let $\mathscr F, \mathscr G$ be $d$-dimensional atlases of class $C^k$ on $M$.
$\mathscr F, \mathscr G$ are '''$C^k$-compatible''' {{iff}} their union $\mathscr F \cup \mathscr G$ is an atlas of class $C^k$.
Category:Definitions/Manifolds
\end{definition}