Theorem 2

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

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

A connected group $G$ in which there exists a neighbourhood of the identity element homeomorphic to an open interval of $\mathbf{R}$ is isomorphic to either $\mathbf{R}$ or $\mathbf{T}$ .

This is an immediate consequence of the preceding theorem, together with Proposition 7 of § 1, no. 4.

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

Cited by

Remark 1, § 3
Remark 2, § 3
Theorem 1, § 4

Cites

Proposition 7 of § 1, no. 4