Remark 3
Tag 07J0, permanent. Cite it as [Bourbaki, Tag 07J0].
Topological Vector Spaces, II, p. 56, § 7. Extremal points and extremal generators
In a Banach space E of infinite dimension, it may happen that the closed ball of centre 0 and radius 1 does not possess any extremal point (II, p. 89, exerc. 14).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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