Bourbaki

Definition 6

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

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

With the preceding notations, one says that σ\sigma is a strong contraction if, moreover, one has r(σ(x,t))=r(x)r(\sigma (x, t)) =r(x) for every x∈Xx\in X and every t∈It\in \mathbf{I},

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, 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.