On y présente trois exemples : un espace bornologique qui contient un sous-espace de codimension infinie dénombrable non infratonnelé, un -espace infratonnelé qui contient un sous-espace de codimension infinie dénombrable qui n’est pas un -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 -space containing a subspace of infinite countable codimension which is not -space, and bornological barrelled space which is not inductive limit of Baire space.
@article{AIF_1972__22_2_21_0, author = {Valdivia, Manuel}, title = {Some examples on quasi-barrelled spaces}, journal = {Annales de l'Institut Fourier}, pages = {21--26}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {22}, number = {2}, year = {1972}, doi = {10.5802/aif.409}, zbl = {0226.46005}, mrnumber = {49 #1053}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.409/} }
TY - JOUR AU - Valdivia, Manuel TI - Some examples on quasi-barrelled spaces JO - Annales de l'Institut Fourier PY - 1972 SP - 21 EP - 26 VL - 22 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.409/ DO - 10.5802/aif.409 LA - en ID - AIF_1972__22_2_21_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.409/
[1] Éléments de Mathématiques, Livre V : Espaces vectoriels topologiques, (ch. III, ch. IV, ch. V), Paris (1964).
,[2] Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math., 25, 50-55 (1952). | MR | Zbl
,[3] Sur les espaces (F) et (DF), Summa Brasil. Math., 3, 57-123 (1954). | MR | Zbl
,[4] Produits tensoriels topologiques et espaces nucléaires Mem. Math. Soc., 16 (1955). | MR | Zbl
,[5] Topological Vector Spaces I, Berlin-Heidelberg-New York, Springer (1969). | MR | Zbl
,[6] A hereditary property in locally convex spaces, Ann. Inst. Fourier, 21, 1-2 (1971). | Numdam | MR | Zbl
,[7] On final topologies, J. Reine angew. Math., 251, 193-199 (1971). | MR | Zbl
,[8] On D F spaces, Math. Ann., 191, 38-43 (1971). | MR | Zbl
,[9] A class of bornological barrelled spaces which are not ultrabornological, Math. Ann. 194, 43-51 (1971). | MR | Zbl
,[10] Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier, 21, 3-13 (1971). | Numdam | MR | Zbl
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