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The Attouch-Wets topology and a characterisation of normable linear spaces

Published online by Cambridge University Press:  17 April 2009

Ľubica Holá
Ľubica Holá
Affiliation:
Department of Probability and Mathematical Statistics, MFF UK, 842 15 Bratislava, Czechoslovakia
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Abstract

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Let X and Y be metric spaces and C(X, Y) be the space of all continuous functions from X to Y. If X is a locally connected space, the compact-open topology on C(X, Y) is weaker than the Attouch-Wets topology on C(X, Y). The result is applied on the space of continuous linear functions. Let X be a locally convex topological linear space metrisable with an invariant metric and X* be a continuous dual. X is normable if and only if the strong topology on X* and the Attouch-Wets topology coincide.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 1 , August 1991 , pp. 11 - 18
Copyright
Copyright © Australian Mathematical Society 1991

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