Example 4

Tag 0B36, permanent. Cite it as [Bourbaki, Tag 0B36].

In a product space

X = \prod_{i \in I} X_i,

each projection

\mathrm{pr}_i : X \to X_i

is a continuous open mapping, but is not necessarily closed (§ 4, no. 2, Proposition 5).

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

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