Rascal finite sets

Abstract

In this paper we consider finite sets in a normed, infinite dimensional space. First, we study the following problem: given a finite set $F$, does there exist a sphere containing $F$ on its surface? We indicate some results and we collect some examples concerning this problem, also for sets of small cardinality. Then we give an example of a three-point set, in a Hilbert space, without incenter.