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Barrelled spaces and dense vector subspaces

Published online by Cambridge University Press:  17 April 2009

W.J. Robertson ,
S.A. Saxon  and
A.P. Robertson
W.J. Robertson
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009
S.A. Saxon
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611, U.S.A.
A.P. Robertson
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, Western Australia 6150, Australia
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Abstract

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This note presents a structure theorem for locally convex barrelled spaces. It is shown that, corresponding to any Hamel basis, there is a natural splitting of a barrelled space into a topological sum of two vector subspaces, one with its strongest locally convex topology. This yields a simple proof that a barrelled space has a dense infinite-codimensional vector subspace, provided that it does not have its strongest locally convex topology. Some further results and examples discuss the size of the codimension of a dense vector subspace.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 383 - 388
Copyright
Copyright © Australian Mathematical Society 1988

References

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