Farthest point problem and M-compact sets
Functional Analysis
2024-07-30 v1
Abstract
In this paper we give an elementary proof of the fact that every uniquely remotal set is singleton in a finite dimensional strictly convex normed linear space. We show that if A is a uniquely remotal M-compact subset with the derived set of A non-empty then the derived set of A is M-compact and uniquely remotal. We also show that if A is a uniquely remotal M-compact set and the derived set of A is compact then A is singleton.
Keywords
Cite
@article{arxiv.1605.04100,
title = {Farthest point problem and M-compact sets},
author = {D. Sain and K. Paul and A. Ray},
journal= {arXiv preprint arXiv:1605.04100},
year = {2024}
}