Description

• Title:
  A partial positive solution to a conjecture of Ricceri
• Creator:
  Garcia-Pacheco, Francisco Javier;
  Hill, Justin R.
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 1 (September 2015); 57 - 67;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.037/7200
• Subject:
  Anti-proximinal;
  barrelled;
  Ricceri;
  Primary;
  15A03;
  46A55;
  Secondary;
  46B20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.037
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other