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Are C^1$C^1$ immersions dense in C^1$C^1$?

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Are C^1 immersions dense in C^1?

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)?