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Quasi-suprabarrelled spaces

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

J. C. Ferrando  and
M. López-Pellicer
J. C. Ferrando
Affiliation:
Departmento de Matemáticas (ETSIA)Universidad PolitécnicaApartado 22012 46022-Valencia, Spain
M. López-Pellicer
Affiliation:
Departmento de Matemáticas (ETSIA)Universidad PolitécnicaApartado 22012 46022-Valencia, Spain
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Abstract

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In this paper a proper class of barrelled spaces which strictly contains the suprabarrelled spaces is considered. A closed graph theorem and some permanence properties are given. This allows us to prove the necessity of a condition of a theorem of S. A. Saxon and P. P. Narayanaswami by constructing an example of a non-suprabarrelled Baire-like space which is a dense subspace of a Fréchet space and is not an (LF)-space under any strong locally convex topology.

Keywords

barrelled space.

MSC classification

Secondary: 46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 137 - 145
Copyright
Copyright © Australian Mathematical Society 1989

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