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Semiconvex spaces

Published online by Cambridge University Press:  18 May 2009

S. O. Iyahen
S. O. Iyahen
Affiliation:
The University, Keele
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Many of the techniques and notions used to study various important theorems in locally convex spaces are not effective for general linear topological spaces. In [4], a study is made of notionsin general linear topological spaces which can be used to replace barrelled, bornological, and quasi-barrelled spaces. The present paper contains a parallel study in the context of semiconvex spaces.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 9 , Issue 2 , July 1968 , pp. 111 - 118
Copyright
Copyright © Glasgow Mathematical Journal Trust 1968

References

REFERENCES

1.Bourbaki, N., Élements de mathématique, Livre V; Espaces vectorials topologiques, Ch. III–V, Actualites Sci. Ind. 1229 (Paris, 1955).Google Scholar
2.Grothendieck, A., Sur les espaces (F) et (DF), Summa Brasil. Math. 3 (1954), 57–123.Google Scholar
3.Husain, T., Two new classes of locally convex spaces, Math. Ann. 166 (1966), 289–299.CrossRefGoogle Scholar
4.Iyahen, S. O., On certain classes of linear topological spaces, Proc. London Math. Soc. (3) 18 (1968), 285–307.CrossRefGoogle Scholar
5.Iyahen, S. O., Some remarks on countably barrelled and countably quasi-barrelled spaces, Proc. Edinburgh Math. Soc. (2) 15 (1967), 295–296.CrossRefGoogle Scholar
6.Kelley, J. L., General topology (New York, 1955).Google Scholar
7.Kelley, J. L. and Namioka, I., Linear topological spaces (New York, 1963).CrossRefGoogle Scholar
8.Klee, V. L., Exotic topologies for linear spaces, Proc. Sympos. general topology and its relation to modern analysis and algebra (Prague, 1961), 238–249.Google Scholar
9.Klee, V. L., Shrinkable neighbourhoods in Hausdorff linear spaces, Math. Ann. 14 (1960), 281–285.CrossRefGoogle Scholar
10.Komura, Y., On linear topological spaces, Kumamoto J. Sci. Ser. A 5 (1962), 148–157.Google Scholar
11.Simons, S., Boundedness in linear topological spaces, Trans. Amer. Math. Soc. 113 (1964), 169–180.CrossRefGoogle Scholar
12.Robertson, W., Completions of topological vector spaces, Proc. London Math. Soc. (3) 8 (1958), 242–257.CrossRefGoogle Scholar
13.Weston, J. D., The principle of equicontinuity for topological vector spaces, Proc. Univ. Durham Philos. Soc. Ser. A 13 (1957), 1–5.Google Scholar