# Homework Help: How a local diffeomorphism preserves orientation

1. Sep 30, 2012

### catellanos

Hi, I'm currently reading Manfredo do Carmo's "Differential Geometry of curves and surfaces" and I'm stocked with problem 2 of section 2-6 which is "Let $S_2$ be an orientable regular surface and $\varphi:S_1 \rightarrow S_2$ be a differentiable map which is a local diffeomorphism at every $p \in S_1$.Prove that $S_1$ is orientable".
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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