Definition:Chart Compatible with Atlas

Definition

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 $A$.