Local Diffeomorphism between Manifolds

Let \(M\) and \(N\) denote smooth manifolds. A smooth map \(F\colon M\to N\) is a local diffeomorphism at a point \(p\in M\), if there exist open subsets \(U\subseteq M\) and \(V\subseteq N\), such that the restriction

\[ F|_U \colon U\to V \]

is a diffeomorphism .