Remark 2

Tag 08BL, permanent. Cite it as [Bourbaki, Tag 08BL].

Functions of a Real Variable, chapter IV, § 1. EXISTENCE THEOREMS

Peano’s theorem no longer holds when $E$ is an arbitrary complete normed space of infinite dimension (IV, p. 204, exerc. 18).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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