\begin{definition}[Definition:Chart]
Let $M$ be a topological manifold of dimension $d$.
A '''$d$-dimensional chart''' of $M$ is an ordered pair $\struct {U, \phi}$, where:
:$U$ is an open subset of $M$
:$\phi: U \to D$ is a homeomorphism of $U$ onto an open subset $D$ of Euclidean space $\R^d$.
\end{definition}