Remark

Tag 079P, permanent. Cite it as [Bourbaki, Tag 079P].

Topological Vector Spaces, I, p. 16, § 2. Linear varieties in a topological vector space

The result of th. 3 is no longer true if K is a discrete division ring as is shown by the example of $\mathbf{R}$ (with the usual topology) considered as a topological vector space over the discrete field $\mathbf{Q}$ .

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

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Cites

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