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The strict topology on a space of vector-valued functions

Published online by Cambridge University Press:  20 January 2009

Liaqat Ali Khan
Liaqat Ali Khan
Affiliation:
Department of Pure Mathematics, University College of Wales, Aberystwyth.
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Let X be a topological space, E a real or complex topological vector space, and C(X, E) the vector space of all bounded continuous E-valued functions on X. The notion of the strict topology on C(X, E) was first introduced by Buck (1) in 1958 in the case of X locally compact and E a locally convex space. In recent years a large number of papers have appeared in the literature concerned with extending the results contained in Buck's paper (1); see, for example, (14), (15), (3), (4), (12), (2), and (6). Most of these investigations have been concerned with generalising the space X and taking E to be the scalar field or a locally convex space.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 1 , February 1979 , pp. 35 - 41
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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