A partial positive solution to a conjecture of Ricceri
DOI:
https://doi.org/10.12775/TMNA.2015.037Słowa kluczowe
Anti-proximinal, barrelled, RicceriAbstrakt
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.Pobrania
Opublikowane
2015-09-01
Jak cytować
1.
GARCIA-PACHECO, Francisco Javier & HILL, Justin R. A partial positive solution to a conjecture of Ricceri. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2015, T. 46, nr 1, s. 57–67. [udostępniono 22.7.2024]. DOI 10.12775/TMNA.2015.037.
Numer
Dział
Articles
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0