Is this vector field really conservative?

Question

Its given the vector field $\textbf{F}(\textbf{r})=c \frac{\textbf{r}}{|\textbf{r}|^3}$ and it's written in my textbook that $\textbf{F}$ is conservative because it has a potential function. However, isn't the vector field undefined at the origin? Would it not interfere with the condition of the region to be simply-connected (so $\textbf{F}$ can be considered conservative)? I may be mixing conditions up, but I would like some help to clarify it.