Bourbaki

Corollary

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

General Topology, chapter VII, § 1. Subgroups and quotient groups of $\mathbf{R}^n$

Every closed subgroup of T\mathbf{T}, other than T\mathbf{T} itself, is a finite cyclic group. Every Hausdorff quotient group of T\mathbf{T}, other than {0}\{0\}, is isomorphic to T\mathbf{T}.

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

Cited by

Nothing.

Cites

Nothing.

Transcribed from the printed volume. Not translated.