Corollary
Tag 04DU, permanent. Cite it as [Bourbaki, Tag 04DU].
Commutative Algebra, chapter III, § 2. General results on filtered rings and modules
The ring B is a topological ring and the B-module F a topological B-module.
The first assertion is obtained by applying Proposition 3 to .
It is seen in particular that a filtered ring A whose filtration is exhaustive is a topological ring; if this is so every filtered A-module whose filtration is exhaustive is a topological A-module.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.