习题 3, § 3

令 $G$ 为（不一定可交换的）线性有序群。 If $G$, endowed with the topology $\mathscr{T}_0(G)$, is locally compact and not discrete, then $G$ is locally isomorphic to $\mathbf{R}$, and the identity component of $G$ is an open subgroup isomorphic to $\mathbf{R}$ (use Exercise 6 of Chapter IV, § 2, and Proposition 2 of § 2).