no. 2
On nonbornological barrelled spaces
Annales de l'Institut Fourier, Volume 22 (1972) no. 2, pp. 27-30

If E is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of E. The same result is obtained replacing “barrelled” by “quasi-barrelled”.

On démontre que si E est le produit topologique d’une famille non dénombrable d’espaces tonnelés de dimension non nulle, il existe un nombre infini de sous-espaces tonnelés de E, qui ne sont pas bornologiques. Un résultat semblable est obtenu si l’on change “tonnelé” en “infratonnelé”.

@article{AIF_1972__22_2_27_0,
     author = {Valdivia, Manuel},
     title = {On nonbornological barrelled spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {27--30},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {22},
     number = {2},
     year = {1972},
     doi = {10.5802/aif.410},
     mrnumber = {49 #1050},
     zbl = {0226.46006},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.410/}
}
TY  - JOUR
AU  - Valdivia, Manuel
TI  - On nonbornological barrelled spaces
JO  - Annales de l'Institut Fourier
PY  - 1972
SP  - 27
EP  - 30
VL  - 22
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://www.numdam.org/articles/10.5802/aif.410/
DO  - 10.5802/aif.410
LA  - en
ID  - AIF_1972__22_2_27_0
ER  - 
%0 Journal Article
%A Valdivia, Manuel
%T On nonbornological barrelled spaces
%J Annales de l'Institut Fourier
%D 1972
%P 27-30
%V 22
%N 2
%I Institut Fourier
%C Grenoble
%U https://www.numdam.org/articles/10.5802/aif.410/
%R 10.5802/aif.410
%G en
%F AIF_1972__22_2_27_0
Valdivia, Manuel. On nonbornological barrelled spaces. Annales de l'Institut Fourier, Volume 22 (1972) no. 2, pp. 27-30. doi: 10.5802/aif.410

[1] N. Bourbaki, Sur certains spaces vectoriels topologiques, Ann. Inst. Fourier, 5-16 (1950). | Zbl | MR | Numdam

[2] J. Dieudonné, Recent development in the theory of locally convex spaces, Bull. Amer. Math. Soc., 59, 495-512 (1953). | Zbl | MR

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

[4] Y. Komura, Some examples on linear topological spaces, Math. Ann., 153, 150-162 (1964). | Zbl | MR

[5] L. Nachbin, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci., USA, 40, 471-474 (1954). | Zbl | MR

[6] T. Shirota, On locally convex vector spaces of continuous functions, Proc. Jap. Acad., 30, 294-298 (1954). | Zbl | MR

Cited by Sources: