ACTA issues

Dispensable points, radial functions, and boundaries of starshaped sets

Guillermo Hansen, Horst Martini

Acta Sci. Math. (Szeged) 80:3-4(2014), 689-699

Abstract. This paper deals with the structure of the boundary of a closed starshaped set in Euclidean space. Based on related results, we derive continuity properties of radial functions of starshaped sets and also new results on dispensable points of such sets. This yields new basic insights in the geometry of starshaped sets, since the notion of dispensable points of starshaped sets is a direct generalization of that of extreme points of convex sets.

DOI: 10.14232/actasm-013-275-5

AMS Subject Classification (1991): 52A07, 52A20, 52A30

Keyword(s): dispensable point, extreme point, infinity cone, opposite cone, radial function, starshaped set, upper semicontinuity

Received April 16, 2013, and in revised form September 12, 2013. (Registered under 25/2013.)