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On B() and Br() locally convex spaces

Published online by Cambridge University Press:  24 October 2008

L. J. Sulley
L. J. Sulley
Affiliation:
University College of Swansea
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Extract

1. Introduction. In his papers (2), (3) and (4), and in his book (5), Husain studied the locally convex, Hausdorff, linear topological spaces (hereafter abbreviated to l.c. spaces) which he called B() spaces and Br() spaces and which satisfy weakened forms of the B completeness and Br completeness conditions of Ptak (8). L.c. spaces satisfying another weakening of the Br completeness condition were studied by Persson in (7) and were called by him, weakly t-polar. We consider some examples in connexion with these spaces.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 95 - 97
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Bourbaki, N.Elements de mathematique, Espaces vectoriels topologiques, Livre V, Chaps. III-V. (Hermann, Paris, 1964.)Google Scholar
(2)Husain, T.Locally convex spaces with the B()-property. Math. Ann. 146 (1962), 413–422.CrossRefGoogle Scholar
(3)Husain, T.B()-spaces and the closed graph theorem. Math. Ann. 153 (1964), 293–298.CrossRefGoogle Scholar
(4)Husain, T.B()-spaces and the closed graph theorem II. Math. Ann. 156 (1964), 334–336.CrossRefGoogle Scholar
(5)Husain, T.The open mapping and closed graph theorems in topological vector spaces (Oxford University Press, Oxford, 1965).CrossRefGoogle Scholar
(6)Kelley, J. L. and Namioka, I.Linear topological spaces (Van Norstrand, Princeton, 1963).CrossRefGoogle Scholar
(7)Persson, A.A remark on the closed graph theorem in locally convex vector spaces. Math. Scand. 19 (1966), 54–58.CrossRefGoogle Scholar
(8)Ptak, V.Completeness and the open mapping theorem. Bull. Soc. Math. France 86 (1958), 41–74.CrossRefGoogle Scholar