Example 1

Tag 04DX, permanent. Cite it as [Bourbaki, Tag 04DX].

Commutative Algebra, chapter III, § 2. General results on filtered rings and modules

Let $G$ be a complete filtered group. Every closed subgroup of $G$ with the induced filtration is complete (General Topology, Chapter II, § 3, no. 4, Proposition 8). Every quotient group of $G$ with the quotient filtration is complete (General Topology, Chapter IX, § 3, no. 1, Remark 1).

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

Cited by

Exercise 17, § 3

Cites

*General Topology*, Chapter II, § 3, no. 4, Proposition 8
*General Topology*, Chapter IX, § 3, no. 1