Let $M$ be $n$-dimensional manifold, $p \in M$, $V$- open neighbourhood of $p$ and let $Y$ be a smooth vector field in $V$.
Do there exist an open neighbourhood $W \subset V$ of $p$ and a smooth vector field $X$ on the whole $M$ which extends $Y|_W$ ? How to do it. I know that similar fact, but for smooth real valued functions instead of smooth vector fields, holds.
Thanks.