Corollary

Tag 07MC, permanent. Cite it as [Bourbaki, Tag 07MC].

Topological Vector Spaces, III, p. 12, § 2. Bornological spaces

Every Hausdorff and semi-complete bornological space is an inductive limit of Banach spaces.

In fact, the spaces E_A, where A is closed and bounded are Banach spaces (III, p. 8, corollary).

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

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