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

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

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

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     title = {The space $D(U)$ is not $B_r$-complete},
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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

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