# Definition:Chart Compatible with Atlas

Let $M$ be a topological space.
Let $A$ be a $d$-dimensional $C^k$-atlas on $M$.
Let $\struct {U, \phi}$ be a $d$-dimensional chart of $M$.
Then $\struct {U, \phi}$ is $C^k$-compatible with $A$ if and only if $\struct {U, \phi}$ is $C^k$-compatible with every chart of $A$.