Definition 1

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

General Topology, chapter III, § 2. Subgroups, quotient groups, homomorphisms homogeneous spaces, product groups

A continuous homomorphism of a topological group $G$ into a topological group $G'$ is said to be a strict morphism of $G$ into $G'$ if the bijective homomorphism $\dot{f}$ of $G/\overline{f^{-1}}(e')$ onto $f(G)$ , associated with $f$ , is an isomorphism of topological groups (in other words, if $\dot{f}$ is bicontinuous).

An isomorphism of a topological group $G$ onto a topological group $G'$ is therefore a bijective strict morphism of $G$ onto $G'$ .

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

Cited by

§ 2. General results on filtered rings and modules

Cites

Nothing.