Corollary 3

Tag 0B43, permanent. Cite it as [Bourbaki, Tag 0B43].

General Topology, chapter I, § 6. Filters

The ordered set of all filters on a non-empty set $X$ is inductive.

For every linearly ordered set $\Phi$ of filters on $X$ satisfies the condition of Corollary 2 of Proposition 1, since the sets $A_i$ all belong to the same $\mathfrak{F}_j$ by hypothesis, and we can apply $(\mathrm{F}_{\mathrm{II}})$ .

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

Cited by

Definition 4, § 6

Cites

Corollary 2 of Proposition 1