Exercise 2, § 3

Let $G$ be a totally ordered group (not necessarily commutative) not reduced to the identity element; the topology $\mathscr{T}_0(G)$ (I, p. 91, exer. 5) is compatible with the group structure of $G$. If, for this topology, $G$ is connected, $G$ is isomorphic to the additive group $\mathbf{R}$ (use exer. 7 of IV, p. 48, and prop. 2 of V, p. 9).