KLEE-PHELPS CONVEX GROUPOIDS

We prove that a pair of proximal Klee-Phelps convex groupoids A(o), B(o) in a finite dimensional normed linear space E are normed proximal, i.e., A(o) delta B(o) if and only if the groupoids are normed proximal. In addition, we prove that the groupoid neighbourhood N-z (o) subset of S-z (o) is convex in E if and only if N-z (o) = S-z (o). (C) 2017 Mathematical Institute Slovak Academy of Sciences