Proposition 4

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

General Topology, chapter VII, § 2. Continuous homomorphisms of $\mathbf{R}^n$ and its quotient groups

If $\varphi$ is the canonical homomorphism of $\mathbf{R}$ onto $\mathbf{T}$ , every continuous homomorphism of $\mathbf{R}$ into $\mathbf{T}$ is of the form $x \mapsto \varphi(ax)$ where $a \in \mathbf{R}$ ; and it is a strict morphism of $\mathbf{R}$ onto $\mathbf{T}$ if $a \neq 0$ .

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

Cited by

Remark, § 2

Cites

Nothing.