diffeomorphism

Definition

A diffeomorphism is a smooth map $f: U \to V$ where $f$ is one-to-one and onto (i.e. one-to-one correspondence), and $f^{-1}: V \to U$ is also smooth.

References

1. http://staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/Lec02.pdf