Bourbaki

Remark 5

Tag 01MO, permanent. Cite it as [Bourbaki, Tag 01MO].

Topologie algébrique, chapter I, § 2. Applications étales

Let Y be a topological space. Let (Ai)i∈I(A_i)_{i\in I} be a family of subsets of Y and let X be the sum space of the family (Ai)i∈I(A_i)_{i\in I}. The canonical mapping of X into Y is separated.

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.

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Cites

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Machine translation of the English, by gpt-5.4, against glossary version 34. Not checked by a person.