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.

@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},
     mrnumber = {49 #1053},
     zbl = {0226.46005},
     language = {en},
     url = {https://www.numdam.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://www.numdam.org/articles/10.5802/aif.409/
DO  - 10.5802/aif.409
LA  - en
ID  - AIF_1972__22_2_21_0
ER  - 
%0 Journal Article
%A Valdivia, Manuel
%T Some examples on quasi-barrelled spaces
%J Annales de l'Institut Fourier
%D 1972
%P 21-26
%V 22
%N 2
%I Institut Fourier
%C Grenoble
%U https://www.numdam.org/articles/10.5802/aif.409/
%R 10.5802/aif.409
%G en
%F AIF_1972__22_2_21_0
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://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

  • References, Barrelled Locally Convex Spaces, Volume 131 (1987), p. 484 | DOI:10.1016/s0304-0208(08)71679-7
  • Valdivia, Manuel On inductive limits of banach spaces, Manuscripta Mathematica, Volume 15 (1975) no. 2, p. 153 | DOI:10.1007/bf01213785
  • Valdivia, Manuel On a class of quasi-barrelled spaces, Mathematische Annalen, Volume 202 (1973) no. 4, p. 295 | DOI:10.1007/bf01433459
  • Horváth, John Locally convex spaces, Summer School on Topological Vector Spaces, Volume 331 (1973), p. 41 | DOI:10.1007/bfb0068227

Cité par 4 documents. Sources : Crossref