Let \(V_{1}\) and \(V_{2}\) be finitely dimensional real vector spaces and \(U_{1}\subseteq V_{1}\) and \(U_{2}\subseteq V_{2}\) open subsets. A function. \[\varphi \colon U_{1}\longrightarrow U_{2}\,\]
is called a \(C^{n}\)-diffeomorphism if \(\varphi \) is bijective and \(n\) times continuously differentiable, and if the inverse function. \[\varphi ^{-1}\colon U_{2}\longrightarrow U_{1}\,\]
is also \(n\) times continuously differentiable.
Definitions: 1