Proposition 2

Tag 0BV1, permanent. Cite it as [Bourbaki, Tag 0BV1].

General Topology, chapter V, § 1. Subgroups and quotient groups of R

The Hausdorff quotient groups of $\mathbf{R}$ , other than $\{0\}$ , are the groups $\mathbf{R}/a\mathbf{Z}$ ( $a \geqslant 0$ ). If $a$ and $b$ are $> 0$ , the automorphism $x \to b/a\,x$ of $\mathbf{R}$ transforms $a\mathbf{Z}$ into $b\mathbf{Z}$ , and therefore (Chapter III, § 2, no. 8, Remark 3) the quotient groups $\mathbf{R}/a\mathbf{Z}$ and $\mathbf{R}/b\mathbf{Z}$ are isomorphic; in other words:

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

Cited by

Nothing.

Cites

Chapter III, § 2, no. 8, Remark 3