> [!definition] > > Let $X$ be a [[Hausdorff Space|Hausdorff]] [[Manifold|manifold]] of class $C^p$, $Y \subset X$ be an [[Immersion|immersed]]/[[Embedding|embedded]] [[Submanifold|submanifold]], and $\xi \in \vf(X)$ be a vector field. Let $p \in Y$, then $\xi$ is **tangent to** $Y$ **at** $p$ if $\xi(p) \in T_pY \subset T_pX$, and is **tangent to** $Y$ if it is tangent to $Y$ at every point.