Exercise 5, § 3

Give an example of a topology on $\mathbf{R}$, compatible with its group structure, for which $\mathbf{R}$ is connected, locally compact, locally connected, and the complement of $\{0\}$ in $\mathbf{R}$ is connected (use the fact that $\mathbf{R}$ and $\mathbf{R}^n$ are algebraically isomorphic).*