Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

By definition (http://en.wikipedia.org/wiki/Local_diffeomorphism), that $f$ is a local diffeomorphism of $M$ means for every point $p$ of $M$, there exists a neighborhood $U$ of $p$ such that $f(U)$ is open and $f|_U:U\rightarrow f(U)$ is a diffeomorphism.

However, I think this definition may imply that $f$ is a global diffeomorphism because by definition of diffeomorphism (in Lee's book Manifolds and differential geometry) which is precisely that $f$ is diffeomorphism at every point.

So, do I miss something?

share|improve this question
4  
You miss that a local diffeomorphism needn't to be bijective, for example $\exp(i\cdot) \colon \mathbb R\to S^1$ is a local diffeomorphism. –  martini Oct 22 '12 at 11:26
    
right....thank you. –  hxhxhx88 Oct 22 '12 at 11:59
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.