POLAR LOCALLY CONVEX TOPOLOGIES AND ATTOUCH-WETS CONVERGENCE

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 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.