Corollary 2

Tag 04E5, permanent. Cite it as [Bourbaki, Tag 04E5].

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

Suppose that one of the following hypotheses holds : $(\alpha)$ X is complete, Y is Hausdorff and its filtration is exhaustive; $(\beta)$ Y is discrete and its filtration is exhaustive. Then, if gr(u) is surjective, u is surjective.

In this case $Y = \bigcup_n Y_n = \bigcup_n u(X_n) \subset u(X)$ .

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

Cited by

Proposition 10, § 2
Proposition 12, § 2

Cites

Nothing.