On superbarrelled spaces. Closed graph theorems.
Baltasar Rodríguez Salinas (1995)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Baltasar Rodríguez Salinas (1995)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Manuel Valdivia (1972)
Annales de l'institut Fourier
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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”.
Stojan Radenović (1986)
Publications de l'Institut Mathématique
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Manuel López Pellicer, Salvador Moll (2003)
RACSAM
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It is well known that some dense subspaces of a barrelled space could be not barrelled. Here we prove that dense subspaces of l∞ (Ω, X) are barrelled (unordered Baire-like or p?barrelled) spaces if they have ?enough? subspaces with the considered barrelledness property and if the normed space X has this barrelledness property. These dense subspaces are used in measure theory and its barrelledness is related with some sequences of unitary vectors. ...
J. Kakol, W. Sliwa, M. Wójtowicz (1994)
Collectanea Mathematica
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M. Gupta, P. K. Kamthan, S. K. Ray (1976)
Colloquium Mathematicae
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Manuel Valdivia (1972)
Annales de l'institut Fourier
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The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled -space containing a subspace of infinite countable codimension which is not -space, and bornological barrelled space which is not inductive limit of Baire space.
Manuel Valdivia (1973)
Publications du Département de mathématiques (Lyon)
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Christopher E. Stuart (1996)
Collectanea Mathematica
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J.C. Ferrando, M. López Pellicer (1998)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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In this note we obtainsome strong barrelledness properties concerning the simple function space generated by the hereditary ring Z of a11 subsets of density zero of N.