On démontre que si 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 , qui ne sont pas bornologiques. Un résultat semblable est obtenu si l’on change “tonnelé” en “infratonnelé”.
If 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 . The same result is obtained replacing “barrelled” by “quasi-barrelled”.
@article{AIF_1972__22_2_27_0,
author = {Valdivia, Manuel},
title = {On nonbornological barrelled spaces},
journal = {Annales de l'Institut Fourier},
volume = {22},
year = {1972},
pages = {27-30},
doi = {10.5802/aif.410},
mrnumber = {49 \#1050},
zbl = {0226.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1972__22_2_27_0}
}
Valdivia, Manuel. On nonbornological barrelled spaces. Annales de l'Institut Fourier, Tome 22 (1972) pp. 27-30. doi : 10.5802/aif.410. http://gdmltest.u-ga.fr/item/AIF_1972__22_2_27_0/
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