A partial positive solution to a conjecture of Ricceri
DOI:
https://doi.org/10.12775/TMNA.2015.037Keywords
Anti-proximinal, barrelled, RicceriAbstract
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 \cite{GPtop} and provides a partial positive solution to a Ricceri's Conjectured posed in \cite{R} with many applications to the theory of partial differential equations. We also study the intrinsic structure of totally anti-proximinal convex subsets proving, among other things, that the absolutely convex hull of a linearly bounded totally anti-proximinal convex set must be finitely open. Finally, a new characterization of barrelledness in terms of comparison of norms is provided.Downloads
Published
2015-09-01
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1.
GARCIA-PACHECO, Francisco Javier and HILL, Justin R. A partial positive solution to a conjecture of Ricceri. Topological Methods in Nonlinear Analysis. Online. 1 September 2015. Vol. 46, no. 1, pp. 57 - 67. [Accessed 28 March 2024]. DOI 10.12775/TMNA.2015.037.
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