Bourbaki

Definition 1

Tag 0792, permanent. Cite it as [Bourbaki, Tag 0792].

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

— A set AA, in a topological vector space EE, is total if, and only if, the closed vector subspace generated by AA coincides with EE (i.e. the set of linear combinations of elements of AA is everywhere dense).

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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Transcribed from the printed volume. Not translated.