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”.

Valdivia, Manuel. On nonbornological barrelled spaces. Annales de l'Institut Fourier, Volume 22 (1972) no. 2, pp. 27-30. doi: 10.5802/aif.410
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