Exercise 4, § 2

If $G$ is compact and if $\widehat{G}$ possesses an element of infinite order, then there exists a continuous nontrivial morphism from $\mathbf{R}$ into G. (Since $\mathbf{R}$ is divisible, there exists a nontrivial morphism from $\widehat{G}$ into $\mathbf{R}.$)