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}, 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 = {http://www.numdam.org/articles/10.5802/aif.410/} }
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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