Vol. 75, No. 1, 1978

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Sets in Rd having (d 2)-dimensional kernels

Marilyn Breen

Vol. 75 (1978), No. 1, 37–44
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 (d2)-dimensional convex set KT S such that every point of T sees KT via S and (aff KT) S = KT. Furthermore, assume that when T is affinely independent, then KT 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
Authors
Marilyn Breen