Corollary 2

Tag 03K5, permanent. Cite it as [Bourbaki, Tag 03K5].

Theory of Sets, chapter III, § 2. Well-ordered sets

Let $\mathfrak{F}$ be a set of subsets of a set E such that, for every subset $\mathfrak{G}$ of $\mathfrak{F}$ which is totally ordered by inclusion, the union (resp. intersection) of the sets of $\mathfrak{G}$ belongs to $\mathfrak{F}$ ; then $\mathfrak{F}$ has a maximal (resp. minimal) element.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Theorem 1, § 4

Cites

Nothing.