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Let $\pi$ be the quotient map $S^n\to\mathbb R\mathrm{P}^n$. Is $\pi_{\star p}:T_pS^n\to T_{\pi(p)}\mathbb R\mathrm P^n$ an isomorphism?
I am trying to prove the following statement:
Let $\pi$ be the quotient map $S^n\to\mathbb R\mathrm{P}^n$. Then $\pi_{\star p}: T_pS^n\to T_{\pi(p)}\mathbb R\mathrm P^n$ an isomorphism
Here is my ...
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