Remark
Tag 07Q5, permanent. Cite it as [Bourbaki, Tag 07Q5].
Topological Vector Spaces, chapter III, § 6. Borel's graph theorem
Recall (III, p. 12) that every homological Hausdorff and semi-complete space, for example every Fréchet space, is the inductive limit of Banach spaces. \* This is also true for the strong dual of a reflexive Fréchet space (IV, p. 23, prop. 4). \*
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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