Remark 2

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

Topological Vector Spaces, IV, p. 16, § 2. Bidual. Reflexive spaces

By remark 3 of IV, p. 5, we can reformulate th. 1 as follows : the Hausdorff space E is semi-reflexive if and only if it is quasi-complete for its weakened topology. If it is semi-reflexive, then it is quasi-complete for its initial topology (IV, p. 5, Remark 2).

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

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