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A variant of separability in dual systems

Published online by Cambridge University Press:  20 January 2009

J. O. Popoola  and
I. Tweddle
J. O. Popoola
Affiliation:
University of Stirling, and University of Lagos
I. Tweddle
Affiliation:
University of Stirling, and University of Lagos
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In (12) we introduced the concept of essential separability and used it to define two classes of locally convex spaces, δ-barrelled spaces and infra-δ-spaces, which serve as domain and range spaces respectively in certain closed graph theorems (12, Theorems 3 and 7). In this note we continue the study of these ideas. The relevant definitions are reproduced below.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 4 , September 1977 , pp. 317 - 327
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

(1) Adasch, N., Tonnelierte Raume und zwei Satze von Banach, Math. Ann. 186 (1970), 209–214.CrossRefGoogle Scholar
(2) Adasch, N., Vollstandigkeit und der Graphensatz, J. Reine Angew. Math. 249 (1971), 217–220.Google Scholar
(3) De Wilde, M. and Houet, C., On increasing sequences of absolutely convex sets in locally convex spaces, Math. Ann. 192 (1971), 257–261.CrossRefGoogle Scholar
(4) Dugundji, J., Topology (Allyn and Bacon, Boston, 1966).Google Scholar
(5) Eberhardt, V., Der Graphensatz von A.P. und W. Robertson fur s-Raume, Manuscripta Math. 4 (1971), 255–262.CrossRefGoogle Scholar
(6) Eberhardt, V., Einige Vererbbarkeitseigenschaften von B-und Br-vollstandigen Raumen, Math. Ann. 215 (1975), 1–11.CrossRefGoogle Scholar
(7) Evans, J. W. and Tapia, R. A., Hamel versus Schauder dimension, Amer. Math. Monthly 77 (1970), 385–388.CrossRefGoogle Scholar
(8) Husain, T., Two new classes of locally convex spaces, Math. Ann. 166 (1966), 289–299.CrossRefGoogle Scholar
(9) Kalton, N. J., Some forms of the closed graph theorem, Proc. Cambridge Philos. Soc. 70 (1971), 401–408.CrossRefGoogle Scholar
(10) Köthe, G., Topological Vector Spaces I (Springer-Verlag, Berlin, 1969).Google Scholar
(11) Noble, N., The continuity of functions on cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187–198.CrossRefGoogle Scholar
(12) Popoola, J. O. and Tweddle, I., On the closed graph theorem, Glasgow Math. J. 17(1976), 89–97.CrossRefGoogle Scholar
(13) Robertson, A. P. and Robertson, W. J., Topological Vector Spaces, 2nd edition (Cambridge University Press, Cambridge, 1973).Google Scholar
(14) Schmets, J., Espaces associes a un espace lineaire a semi-normes-applications aux espaces de fonctions continues (Universite de Liege, 1972–3).Google Scholar
(15) Tweddle, I., Unconditional convergence and bases, Proc. Edinburgh Math. Soc. 18 (Series II) (1973), 321–324.CrossRefGoogle Scholar
(16) Valdivia, M., Some criteria for weak compactness, J. Reine Angew. Math. 255 (1972), 165–169.Google Scholar
(17) Yosida, K. and Hewitt, E., Finitely additive measures,Trans. Amer. Math. Soc. 72 (1952), 46–66.CrossRefGoogle Scholar