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On the stability of barrelled topologies, III

Published online by Cambridge University Press:  17 April 2009

W.J. Robertson ,
I. Tweddle  and
F.E. Yeomans
W.J. Robertson
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia;
I. Tweddle
Affiliation:
Department of Mathematics, University of Stirling, Stirling FK9 4LA, Scotland.
F.E. Yeomans
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia;
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Abstract

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Let E be a barrelled space with dual F ≠ E*. It is shown that F has uncountable codimension in E*. If M is a vector subspace of E* of countable dimension with M ∩ F = {o}, the topology τ(E, F+M) is called a countable enlargement of τ(E, F). The results of the two previous papers are extended: it is proved that a non-barrelled countable enlargement always exists, and sufficient conditions for the existence of a barrelled countable enlargement are established, to include cases where the bounded sets may all be finite dimensional. An example of this case is given, derived from Amemiya and Kōmura; some specific and general classes of spaces containing a dense barrelled vector subspace of codimension greater than or equal to c are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1980 , pp. 99 - 112
Copyright
Copyright © Australian Mathematical Society 1980

References

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