homework and exercises - Magnetic monopole and vector potential

Does anyone know how to prove (in a simple way if possible) that it is impossible to define a single-valued globally defined magnetic vector potential $\vec{A}$ on the manifold $M=\mathbb{R}^3\backslash\{0\}$ for a static magnetic monopole placed at the origin?

Hypothesis: $\vec{B} = g \vec{r}/(4\pi r^3)$