Sets in R^d having (d − 2)-dimensional kernels

Marilyn Breen

Vol. 75 (1978), No. 1, 37–44

DOI: 10.2140/pjm.1978.75.37

Abstract

Let S be a d-dimensional set, d ≧ 2, and assume that for every (d + 1)-member subset T of S, there corresponds a (d− 2)-dimensional convex set K_T ⊆ S such that every point of T sees K_T via S and (aff K_T) ∩ S = K_T. Furthermore, assume that when T is affinely independent, then K_T is the kernel of T relative to S. Then S is starshaped and the kernel of S is (d − 2)-dimensional.

Mathematical Subject Classification 2000

Primary: 52A30

Milestones

Received: 10 January 1977

Revised: 10 June 1977

Published: 1 March 1978