# Definition Given a [[Manifold]] $M$, a *coordinate chart*, or simply a *chart*, is an [[Open Set|open]] [[neighborhood]] $U$ of a point $P\in M$ with the [[Types of Maps|bijection]] $f:U\rightarrow \mathbb{R}^n$. That is, the chart is $(U, f)$. Note that in the definition of a chart above, it is important to observe that the [[neighborhood]] $U$ does not necessarily include all of $M$, and in general it can't. In general, each [[neighborhood]] has its own [[map]] (so that a [[Manifold]] is covered by multiple charts), and each point in $M$ must lie in at least one such [[neighborhood]]. It is easy to see that these neighborhoods (since they are open by definition) must overlap so that they can cover the whole [[Manifold]].