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On the lifting of bounded sets in Fréchet spaces

Published online by Cambridge University Press:  20 January 2009

José Bonet  and
Susanne Dierolf
José Bonet
Affiliation:
Universidad Politécnica de Valencia, Departamento de matématica Aplicada, E.T.S. Arquitectura, E-46071 Valencia, Spain
Susanne Dierolf
Affiliation:
FB Mathematik IV, Universität Trier, Postfach 3825, D-5500 Trier, Germany
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Abstract

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This paper considers the behaviour of a quotient map between Fréchet spaces concerning the lifting of bounded sets. The main result shows that a quotient map between Fréchet spaces that lifts bounded sets with closure (or equivalently such that its strong transpose is a topological isomorphism) must also lift bounded sets without closure.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 2 , June 1993 , pp. 277 - 281
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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