An approach to a Ricceri's conjecture
type: Item
instance of: scholarly article
title: An approach to a Ricceri's conjecture
zbMATH Open document ID: 1264.46008
published in: Topology and its Applications
publication date: 2012-09-19T00:00:00Z
review text: Let \(X\) be a normed space. For \(x\in X\), let \(d(x;A) = \inf \{\| x -e \| : e \in A\}\). A subset \(A\) of \(X\) is said to be anti-proximinal if for all \(x\in X\backslash A\), \(d(x;A)\) is not attained. \(A\) is called totally anti-proximinal if this property holds true for any norm on \(X\). A normed space \(X\) is said to have the anti-proximinal property if every totally anti-proximinal set in \(X\) is not rare. The Ricceri conjecture states ``there exists a non-complete normed space with the anti-proximinal property''. The author proves a result which can be considered a positive result in the direction of solving the Ricceri conjecture.
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 6084118
zbMATH Keywords: anti-proximinal set
zbMATH Keywords: barrelled space
zbMATH Keywords: Ricceri conjecture
Wikidata QID: Q123363943
author: Francisco García-Pacheco
MaRDI profile type: Publication
full work available at URL: j.topol.2012.07.010
OpenAlex ID: W2003686786
cites work: Q3759347
cites work: Non-continuous linear functionals on topological vector spaces
cites work: ISOMETRIC REFLECTIONS IN TWO DIMENSIONS AND DUAL L1-STRUCTURES
cites work: Q4378144
cites work: Every Countable-Codimensional Subspace of a Barrelled Space is Barrelled
DOI: 10.1016/J.TOPOL.2012.07.010
reviewed by: R. Khalil
description: scientific article; zbMATH DE number 6084118