Open Ball is Path-Connected

Theorem
Let $V$ be a normed vector space with norm $\norm {\,\cdot\,}$ over $\R$ or $\C$.

An open ball in the metric induced by $\norm {\,\cdot\,}$ is path-connected.

Proof
Follows from:
 * Open Ball is Convex Set
 * Normed Vector Space is Hausdorff Topological Vector Space
 * Convex Set is Path-Connected