Corollary

Tag 03I2, permanent. Cite it as [Bourbaki, Tag 03I2].

Theory of Sets, chapter II, § 4. Union and intersection of a family of sets

Let $(X_\iota)_{\iota \in I}$ be a family of sets such that $X_\iota = X_\varkappa$ for each pair of indices $(\iota, \varkappa)$ . Then for each $\alpha \in I$ we have

\bigcup_{\iota \in I} X_\iota = X_\alpha, \qquad \textit{and (if } I \neq \emptyset) \qquad \bigcap_{\iota \in I} X_\iota = X_\alpha.

Apply Proposition 1 to the constant mapping $\iota \to \alpha$ of I onto $\{\alpha\}$ .

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

Nothing.

Cites

Proposition 1