Corollary
Tag 07LM, permanent. Cite it as [Bourbaki, Tag 07LM].
Topological Vector Spaces, chapter III, § 1. Bornology in a topological vector space
— If A is semi-complete (in particular, complete) then EA is a Banach space.* In fact, a Cauchy sequence in E_A is also a Cauchy sequence for the topology of E and is contained in a set homothetic to A, hence converges in E.
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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