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On the Stability of Barrelled Topologies II

Published online by Cambridge University Press:  18 May 2009

I. Tweddle  and
F. E. Yeomans
I. Tweddle
Affiliation:
University of Stirling, Stirling, FK9 4LA
F. E. Yeomans
Affiliation:
University of Western Australia, Nedlands, W. Australia6009
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If E is a Hausdorff barrelled space, which does not already have its finest locally convex topology, then the continuous dual E′ may be enlarged within the algebraic dual E*. Robertson and Yeomans [10] have recently investigated whether E can retain the barrelled property under such enlargements. Whereas finite-dimensional enlargements of the dual preserve barrelledness, they have shown that this is not always so for countable-dimensional enlargements E′+M. In fact, if E contains an infinitedimensional bounded set, there always exists a countable-dimensional M for which the Mackey topology τ(E, E′+M) is not barrelled [10, Theorem 2].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 91 - 95
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

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