Remark
Tag 07A5, permanent. Cite it as [Bourbaki, Tag 07A5].
Topological Vector Spaces, chapter I, § 3. Metrisable topological vector spaces
One of the most important classes of metrisable vector spaces are the normed spaces (I, p. 3). But it must be noted that there exist metrisable vector spaces whose topology cannot be defined by a norm (I, § 3, exerc. 1); we shall study important examples later.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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