Proposition 5

Tag 03Q9, permanent. Cite it as [Bourbaki, Tag 03Q9].

Theory of Sets, chapter II, § 5. Product of a family of sets

Let $(X_\iota)_{\iota\in I}$ be a family of sets and let $J$ be a subset of $I$ . If for each $\iota\in I$ we have $X_\iota\ne\varnothing$ , the projection $\operatorname{pr}_J$ is a mapping of $\displaystyle\prod_{\iota\in I}X_\iota$ onto $\displaystyle\prod_{\iota\in J}X_\iota$ .

In view of the remarks made above, it is enough to prove the following proposition :

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

Corollary 1, § 5

Cites

Nothing.