Abstract
N. Bourbaki, [1, p. 35], notices that it is not known if every bornological barrelled space is ultrabornological. In this paper we prove that if E is the topological product of an infinite family of bornological barrelled spaces, of non-zero dimension, there exists an infinite number of bornological barrelled subspaces ofE, which are not ultrabornological. We also give some examples of barrelled normable spaces which are not ultrabornological.
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References
Bourbaki, N.: Elements de mathématiques. Libre V: Espaces vectoriels topologiques (Ch. III, Ch. IV, Ch. V). Paris: Hermann 1964.
Köthe, G.: Topological vector spaces I. Berlin-Heidelberg-New York: Springer 1969.
Valdivia, M.: On final topologies. J. reine angew. Math. (to appear).
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Supported in part by the “Patronato para el Fomento de la Investigación en la Universidad”.
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Valdivia, M. A class of bornological barrelled spaces which are not ultrabornological. Math. Ann. 194, 43–51 (1971). https://doi.org/10.1007/BF01351821
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DOI: https://doi.org/10.1007/BF01351821