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Bounded generators in linear topological spaces

Published online by Cambridge University Press:  18 May 2009

S. O. Iyahen
S. O. Iyahen
Affiliation:
University Of Ibadan, Nigeria
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Ito and Seidman in [5] define a BG space as a locally convex space in whichthere exists a bounded set with a dense span. In this note we extend the idea to a class of not necessarily locally convex linear topological spaces (l.t.s.). We note the link between the idea of a BG space and Weston’s characterization in [7] of separable Banach spaces. Finally we examine σ-BG spaces; here the bounded set in the definition of a BG space is replaced by the union of a sequence of bounded sets.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 12 , Issue 2 , September 1971 , pp. 105 - 109
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

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