English

Klee-Phelps Convex Groupoids

Group Theory 2014-11-05 v1

Abstract

We prove that a pair of proximal Klee-Phelps convex groupoids A()A(\circ),B()B(\circ) in a finite-dimensional normed linear space EE are normed proximal, {\em i.e.}, A() δ B()A(\circ)\ \delta\ B(\circ) if and only if the groupoids are normed proximal. In addition, we prove that the groupoid neighbourhood Nz()Sz()N_z(\circ)\subseteq S_z(\circ) is convex in EE if and only if Nz()=Sz()N_z(\circ) = S_z(\circ).

Cite

@article{arxiv.1411.0934,
  title  = {Klee-Phelps Convex Groupoids},
  author = {J. F. Peters and M. A. Öztürk and M. Uçkun},
  journal= {arXiv preprint arXiv:1411.0934},
  year   = {2014}
}
R2 v1 2026-06-22T06:47:41.826Z