Vol. 53, No. 2, 1974

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

N. Stavrakas

Vol. 53 (1974), No. 2, 627–628

Let S be a compact subset of Ra,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
Received: 9 November 1973
Published: 1 August 1974
N. Stavrakas