# Definition A *diffeomorphism* is a $C^\infty$ ([[Differentiable Function|differentiable]]) [[Types of Maps|bijection]] from one [[manifold]] $M$ into another $N$, and whose inverse is also $C^\infty$. This is called a *diffeomorphism* of $M$ onto $N$ and $M$ and $N$ are said to be *diffeomorphic*.