Bourbaki

Example 5

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

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

We shall prove later (TA, V) that the Euclidean spheres Sn,n⩾1\mathbf{S}_n,n\geqslant 1, are not spaces homotopic to a point. The unit sphere of a Hilbert space of countable type and infinite dimension is contractible at each of its points (EVT, V, p. 71, exerc. 13).

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.