Example 1

Tag 02J3, permanent. Cite it as [Bourbaki, Tag 02J3].

Théories spectrales, chapter II, § 1. Transformation de Fourier

Let $f: H\rightarrow$ G be a strict injective morphism whose image is a distinguished subgroup. The sequence

1\rightarrow H\overset{f}{\longrightarrow}G\overset{p}{\longrightarrow}G/f(H)\rightarrow 1

where $p$ is the canonical projection, is exact. In particular, if H is a closed distinguished subgroup of G, the sequence of topological groups

1\rightarrow H\overset{j}{\longrightarrow}G\overset{p}{\longrightarrow}G/H\rightarrow 1

where $j$ is the inclusion and $p$ the canonical projection, is exact.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.