Corollary 2
Tag 07LB, permanent. Cite it as [Bourbaki, Tag 07LB].
Topological Vector Spaces, chapter III, § 1. Bornology in a topological vector space
— Let E = \prod{i \in I} E_i be the product of a family of locally convex spaces. Then a subset of E is bounded if and only if all its projections are bounded.*
More generally :
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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