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Ultrabarrelled groups and the closed graph theorem

Published online by Cambridge University Press:  24 October 2008

S. O. Iyahen
S. O. Iyahen
Affiliation:
University of Ibadan, Ibadan, Nigeria
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Extract

Suppose that t is a group homomorphism from a topological group E into a topological group F. When is it true, that the closure of t−1(V) in E is a neighbourhood of the identity in E for every neighbourhood V of the identity in F? This question arises naturally in the study of the closed graph theorem in the context of topological groups; for example, see (1) and ((3), p. 213). The concept of a g-ultrabarrelled space introduced in this paper is the result of an investigation aimed at answering this question.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 53 - 58
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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