On B r -completeness
Annales de l'Institut Fourier, Volume 25 (1975) no. 2, pp. 235-248.

In this paper it is proved that if {E n } n=1 and {F n } n=1 are two sequences of infinite-dimensional Banach spaces then H= n=1 E n × n=1 F n is not B r -complete. If {E n } n=1 and {F n } n=1 are also reflexive spaces there is on H a separated locally convex topology , coarser than the initial one, such that H[] is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on B r -completeness and bornological spaces.

Dans le présent article il est démontré que si {E n } n=1 et {F n } n=1 sont deux suites d’espaces de Banach de dimension infinie, alors H= n=1 E n × n=1 F n n’est pas B r -complet. Il est démontré aussi que si {E n } n=1 et {F n } n=1 sont de plus des espaces réflexifs il y a sur H une topologie localement convexe et séparée moins fine que l’initiale, telle que H[] est un espace tonnelé et bornologique, qui n’est pas limite inductive d’espaces de Baire. On donne aussi d’autres résultats sur la B r -complétude et les espaces bornologiques.

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Valdivia, Manuel. On $B_r$-completeness. Annales de l'Institut Fourier, Volume 25 (1975) no. 2, pp. 235-248. doi : 10.5802/aif.564. http://archive.numdam.org/articles/10.5802/aif.564/

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