Bourbaki

Theorem 1 (Brouwer)

Tag 02ON, permanent. Cite it as [Bourbaki, Tag 02ON].

Théories spectrales, chapter III, § 1. Applications linéaires compactes

Let B be a nonempty compact convex subset of a finite-dimensional normed vector space. Every continuous mapping of B into B has a fixed point.

We shall deduce from it the following result.

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

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Cites

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Machine translation of the English, by gpt-5-6-mini, gpt-5-mini, gpt-5.4, 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.