The number of farthest points

The Mazur Intersection Property and Farthest Points

K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.

Further results on multiple coverings of the farthest-off points

Multiple coverings of the farthest-off points ((R,μ)-MCF codes) and the corresponding (ρ, μ)-saturating sets in projective spaces PG(N, q) are considered. We propose some methods which allow us to obtain new small (1, μ)-saturating sets and short (2, μ)-MCF codes with μ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1+1/cq, c ≥ 1). In par...

A note on multiple coverings of the farthest-off points

In this work we summarize some recent results, to be included in a forthcoming paper [1]. We define μ-density as a characteristic of quality for the kind of coverings codes called multiple coverings of the farthest-off points (MCF). A concept of multiple saturating sets ((ρ, μ)-saturating sets) in projective spaces PG(N, q) is introduced. A fundamental relationship of these sets with MCF is sho...

On co-Farthest Points in Normed Linear Spaces

In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...

Farthest Neighbors and Center Points in the Presen