Corollary 1

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

General Topology, chapter II, § 3. Complete spaces

For each $x \in X$ , the neighbourhood filter $\mathfrak{B}(x)$ of $x$ in $X$ is a minimal Cauchy filter.

Take $\mathfrak{F}$ in Proposition 5 to be the filter of all subsets of $X$ which contain $x$ , and take $\mathfrak{B}$ to consist of the single element $\{x\}$ .

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

Cited by

Theorem 3, § 3

Cites

Proposition 5