Remark 3

Tag 0BVR, permanent. Cite it as [Bourbaki, Tag 0BVR].

General Topology, chapter V, § 3. Topological characterization of the groups R and T

The preceding topological characterization of the groups $\mathbf{R}$ and $\mathbf{T}$ involves the topological space $\mathbf{R}$ as an auxiliary set. It is possible to characterize the topological group structures of $\mathbf{R}$ and $\mathbf{T}$ by means of axioms which do not involve any auxiliary set (see Exercises 4 and 5).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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