Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

On the lifting of bounded sets in Fréchet spaces

José Boneta1 and Susanne Dierolfa2

a1 Universidad Politécnica de Valencia, Departamento de matématica Aplicada, E.T.S. Arquitectura, E-46071 Valencia, Spain

a2 FB Mathematik IV, Universität Trier, Postfach 3825, D-5500 Trier, Germany

Abstract

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.

(Received May 31 1991)