This is an announcement for the paper "On the existence of 1-separated sequences on the unit ball of a finite dimensional Banach space" by Eytyhios Glakousakis and Sophocles Mercourakis.

Abstract: Given a finite dimensional Banach space X with dimX = n and an Auerbach basis of X, it is proved that: there exists a set D of n + 1 linear combinations (with coordinates 0, -1, +1) of the members of the basis, so that each pair of different elements of D have distance greater than one.

Archive classification: math.FA math.CO math.MG

Submitted from: smercour@math.uoa.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1312.2896

or

http://arXiv.org/abs/1312.2896