A note on starshaped sets, (k)-extreme points and the half ray property

N. Stavrakas

Vol. 53 (1974), No. 2, 627–628

DOI: 10.2140/pjm.1974.53.627

Abstract

Let S be a compact subset of R^a,d ≧ 2.S is said to have the half-ray property if for each point x of the complement of S there exists a half line with x as vertex having empty intersection with S. It is proven that S is starshaped iff S has the half-ray property and the intersection of the stars of the (d − 2)-extreme points is not empty.

Mathematical Subject Classification 2000

Primary: 52A30

Milestones

Received: 9 November 1973

Published: 1 August 1974