Points of Riemannian Manifold are Contained in Geodesically Convex Geodesic Balls

Theorem
Let $\struct {M, g}$ be a Riemannian manifold.

Let $\epsilon_0 \in \R_{> 0}$.

Then for all $p \in M$ there exists a closed geodesic ball or open geodesic ball centered at $p \in M$ of radius $\epsilon \le \epsilon_0$ which is also geodesically convex.