Abstract:In this manuscript we introduce a new class of convex sets called quasi-absolutely convex and show that a Hausdorff locally convex topological vector space satisfies the weak anti-proximinal property if and only if every totally anti-proximinal quasi-absolutely convex subset is not rare. This improves results from [7] and provides a partial positive solution to a Ricceri's Conjectured posed in [9] with many applications to the theory of partial differential equations. We also study the intrinsic structure of t… Show more
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