Some examples on quasi-barrelled spaces
Annales de l'Institut Fourier, Tome 22 (1972) no. 2, pp. 21-26.

On y présente trois exemples : un espace bornologique qui contient un sous-espace de codimension infinie dénombrable non infratonnelé, un 𝒟ℱ-espace infratonnelé qui contient un sous-espace de codimension infinie dénombrable qui n’est pas un 𝒟ℱ-espace et un espace tonnelé bornologique qui n’est pas limite inductive d’espaces de Baire.

The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled 𝒟ℱ-space containing a subspace of infinite countable codimension which is not 𝒟ℱ -space, and bornological barrelled space which is not inductive limit of Baire space.

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Valdivia, Manuel. Some examples on quasi-barrelled spaces. Annales de l'Institut Fourier, Tome 22 (1972) no. 2, pp. 21-26. doi : 10.5802/aif.409. http://www.numdam.org/articles/10.5802/aif.409/

[1] N. Bourbaki, Éléments de Mathématiques, Livre V : Espaces vectoriels topologiques, (ch. III, ch. IV, ch. V), Paris (1964).

[2] J. Dieudonné, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math., 25, 50-55 (1952). | MR | Zbl

[3] A. Grothendieck, Sur les espaces (F) et (DF), Summa Brasil. Math., 3, 57-123 (1954). | MR | Zbl

[4] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires Mem. Math. Soc., 16 (1955). | MR | Zbl

[5] G. Kothe, Topological Vector Spaces I, Berlin-Heidelberg-New York, Springer (1969). | MR | Zbl

[6] M. Valdivia, A hereditary property in locally convex spaces, Ann. Inst. Fourier, 21, 1-2 (1971). | Numdam | MR | Zbl

[7] M. Valdivia, On final topologies, J. Reine angew. Math., 251, 193-199 (1971). | MR | Zbl

[8] M. Valdivia, On D F spaces, Math. Ann., 191, 38-43 (1971). | MR | Zbl

[9] M. Valdivia, A class of bornological barrelled spaces which are not ultrabornological, Math. Ann. 194, 43-51 (1971). | MR | Zbl

[10] M. Valdivia, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier, 21, 3-13 (1971). | Numdam | MR | Zbl

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