\begin{definition}[Definition:Atlas/Maximal Atlas/Definition 3]
Let $M$ be a topological space.
Let $A$ be a $d$-dimensional atlas of class $C^k$ of $M$.
$A$ is a '''maximal $C^k$-atlas''' {{iff}} $A$ is a maximal element of some differentiable structure, partially ordered by inclusion. That is, a maximal element of some equivalence class of the set of atlases of class $\CC^k$ on $M$ under the equivalence relation of compatibility.
Category:Definitions/Manifolds
\end{definition}