Definition:Chart Compatible with Atlas

Definition
Let $M$ be a topological space.

Let $A$ be a $d$-dimensional $C^k$-atlas on $M$.

Let $(U,\phi)$ be a $d$-dimensional chart of $M$.

Then $(U,\phi)$ is $C^k$-compatible with $A$ $(U,\phi)$ is $C^k$-compatible with every chart of $A$.