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Every countable-codimensional subspace of a barrelled space is barrelled. (English) Zbl 0212.14105

MSC:
46A08 Barrelled spaces, bornological spaces
46A45 Sequence spaces (including Köthe sequence spaces)
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[1] Ichiro Amemiya and Yukio Kōmura, Über nicht-vollständige Montelräume, Math. Ann. 177 (1968), 273 – 277 (German). · Zbl 0157.43903 · doi:10.1007/BF01350719 · doi.org
[2] N. Bourbaki, Eléments de mathématique. XVIII. Première partie: Les structures fondamentales de l’analyse. Livre V: Espaces vectoriels topologiques. Chapitre III: Espaces d’applications linéaires continues. Chapitre IV: La dualité dans les espaces vectoriels topologiques. Chapitre V: Espaces hilbertiens, Actualités Sci. Ind., no. 1229, Hermann & Cie, Paris, 1955 (French). · Zbl 0066.35301
[3] J. Dieudonné, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math. 25 (1952), 50 – 55 (1953) (French). · Zbl 0049.08202
[4] R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. · Zbl 0182.16101
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[6] Tosio Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261 – 322. · Zbl 0090.09003 · doi:10.1007/BF02790238 · doi.org
[7] Gottfried Köthe, Die Bildräume abgeschlossener Operatoren, J. Reine Angew. Math. 232 (1968), 110 – 111 (German). · Zbl 0157.21003 · doi:10.1515/crll.1968.232.110 · doi.org
[8] Mark Levin and Stephen Saxon, A note on the inheritance of properties of locally convex spaces by subspaces of countable codimension, Proc. Amer. Math. Soc. 29 (1971), 97 – 102. · Zbl 0212.14104
[9] S. Saxon, Basis cone base theory, Dissertation, Florida State University, Tallahassee, Fla., 1969 (unpublished).
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