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

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”.

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”.

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     author = {Valdivia, Manuel},
     title = {On nonbornological barrelled spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {27--30},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {22},
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Valdivia, Manuel. On nonbornological barrelled spaces. Annales de l'Institut Fourier, Tome 22 (1972) no. 2, pp. 27-30. doi : 10.5802/aif.410. http://www.numdam.org/articles/10.5802/aif.410/

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