Example of smooth function of a smooth submanifold cannot be obtained by restriction of a smooth function in the manifold

Question

Anyone can give the example of smooth function of a smooth submanifold N of M cannot be obtained by restriction of a smooth function in the smooth manifold M?

Answer 1

Consider the function $f(x) := \frac{1}{x}$ on the smooth submanifold $\Bbb R_+ := (0, \infty)$ of the smooth manifold $\Bbb R$. Since $\lim_{x \to 0^+} = +\infty$, $f$ cannot even be extended continuously to any proper superset of $\Bbb R_+$ in $\Bbb R$.