$V$ is $C^1$ and $V(x_0)=0$ and $ \nabla V $ is not zero $\{ x : V(x)= c \}$ is a surface with no edge around $x_0$

Question

I am studying lyapanov second method in stablity theory of ODE. I have encountered a geometric lemma which says the following:

Assume $ V:\mathbb R^n \to \mathbb R$ is a $C^1$ and $x_0 \in \mathbb R^n $ is such that $V(x_0)=0$. If $ \nabla V $ is not zero in a neighbourhood of $x_0$ then for some small $c$ the set $\{ x : V(x)= c \}$ is a surface with no edge around $x_0$.

I know this is a 2-dimensional smooth manifold , but how could I show that it is has no edge. Thanks! .