Let $M$ be a closed compact manifold.
Is the space of all $C^1$ immersions from $M$ to $\mathbb{R}^m$ ($m> \dim M$) dense in $C^1(M; \mathbb{R}^m)$ (in the $C^1$ topology)?
Are $C^1$ immersions dense in $C^1$?
TYp
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