Injective immersion (between smooth manifolds) that is no homeomorphism onto its image Is there an injective immersion between smooth manifolds that is no homeomorphism onto its image? With smooth I mean $C^\infty$-manifolds and of course also the immersion should be $C^\infty$.

There is an injective immersion of $\mathbb{R}$ into the plane, whose image is the figure 8. Clearly it it not an homeomorphism to its image (since this is not a manifold). 
See also: http://en.wikipedia.org/wiki/Immersed_submanifold#Immersed_submanifolds
