The space D(U) is not Br-complete
Annales de l'Institut Fourier, Tome 27 (1977) no. 4, pp. 29-43.

On étudie quelques classes d’espaces localement convexes avec quotients séparés et non-complets et en conséquence on obtient des résultats de Br-complétude. En particulier, l’espace de L. Schwartz D(Ω) n’est pas Br-complet, où Ω représente un ensemble non-vide de l’espace euclidien Rm.

Certain classes of locally convex space having non complete separated quotients are studied and consequently results about Br-completeness are obtained. In particular the space of L. Schwartz D(Ω) is not Br-complete where Ω denotes a non-empty open set of the euclidean space Rm.

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Valdivia, Manuel. The space $D(U)$ is not $B_r$-complete. Annales de l'Institut Fourier, Tome 27 (1977) no. 4, pp. 29-43. doi : 10.5802/aif.671. https://www.numdam.org/articles/10.5802/aif.671/

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