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Polar locally convex topologies and Attouch-Wets convergence
Published online by Cambridge University Press: 17 April 2009
Abstract
Let X be a Hausdorff locally convex space. We show that convergence of a net of continuous linear functionals on X with respect to a given polar topology on its continuous dual X′ can be explained in terms of the convergence of the corresponding net of its graphs in X × R, and the corresponding net of level sets at a fixed height in X, with respect to a natural generalisation of Attouch-Wets convergence in normable spaces.
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- Copyright © Australian Mathematical Society 1992
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