Definition 2

Tag 0794, permanent. Cite it as [Bourbaki, Tag 0794].

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

— A family $(a_i)_{i \in I}$ of points of a topological vector space $E$ is called topologically independent if for any $\kappa \in I$ , the closed vector subspace generated by the $a_i$ , with $i \neq \kappa$ , does not contain $a_\kappa$ .

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

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