# Embedding of smooth manifolds

1. Mar 4, 2014

### center o bass

Consider a smooth map $F: M \to N$ between two smooth manifolds $M$ and $N$. If the pushforward $F_*: T_pM \to T_{F(p)} N$ is injective and $F$ is a homeomorphism onto $F(M)$ we say that $F$ is a smooth embedding.

In analogy with a topological embedding being defined as a map that is homemorphic onto it's image I would think that an embedding of smooth manifolds would require that $F$ be a diffeomorphism. So my question is; is the definition above equivalent with $F$ being a diffeomorphism between $M$ and $N$.