Bourbaki

Definition 3

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

Topologie algébrique, chapter III, § 1. Homotopies, homéotopies

One says that topological spaces X and Y are homotopy equivalent if there exists a homotopy equivalence of X into Y.

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

Nothing.

Machine translation of the English, by gpt-5.4, gpt-5-6-mini, gpt-5-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.