Vol. 62, No. 1, 1976

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On starshaped sets and Helly-type theorems

John David Baildon and Ruth Silverman

Vol. 62 (1976), No. 1, 37–41
Abstract

Suppose an ordered pair of sets (S,K) in a linear topological space is of Helly type (n + 1,n), i.e., for every n + 1 distinct points in S there is a point in K which sees at least n of them via S. Then if S is closed, K compact, and n 3, the nontrivial visibility sets in K are pairwise nondisjoint. Sufficient conditions are obtained for S to be starshaped.

Mathematical Subject Classification 2000
Primary: 52A30
Secondary: 52A35
Milestones
Received: 2 July 1975
Revised: 9 October 1975
Published: 1 January 1976
Authors
John David Baildon
Ruth Silverman