Theorem 3

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

Théories spectrales, chapter III, § 4. Perturbations dans les espaces de Banach

Let $n$ be a positive integer, V a real normed vector space of dimension $n+ 1$ and W a vector subspace of V of dimension $n$ . Let S be the unit sphere of V. There does not exist a continuous mapping $f: S\rightarrow W$ such that $\|f(x)-x)\|<1$ for all $x\in S$ .

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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