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 [itex] S_2 [/itex] be an orientable regular surface and [itex] \varphi:S_1 \rightarrow S_2 [/itex] be a differentiable map which is a local diffeomorphism at every [itex]p \in S_1 [/itex].Prove that [itex] S_1 [/itex] is orientable".(adsbygoogle = window.adsbygoogle || []).push({});

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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# Homework Help: How a local diffeomorphism preserves orientation

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