Remark
Tag 079E, permanent. Cite it as [Bourbaki, Tag 079E].
Topological Vector Spaces, chapter I, § 2. Linear varieties in a topological vector space
— There are examples of normed topological vector spaces over a complete non-discrete valued division ring, in which every continuous linear form is identically zero (I, p. 25, exerc. 4); in such a space therefore, every hyperplane is everywhere dense (I, p. 11, corollary).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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