Proposition 4

Tag 0B47, permanent. Cite it as [Bourbaki, Tag 0B47].

General Topology, chapter I, § 6. Filters

On a set $X$ , a filter $\mathfrak{F}'$ with base $\mathfrak{B}'$ is finer than a filter $\mathfrak{F}$ with base $\mathfrak{B}$ if and only if every set of $\mathfrak{B}$ contains a set of $\mathfrak{B}'$ .

This is an immediate consequence of Definitions 2 and 3.

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

Cited by

§ 6. Filters
Definition 1, § 7

Cites

Nothing.