Abstract convex sets with respect to the class of general min-type functions

Abstract

In this article we investigate subsets of n-dimensional Euclidean space R ⁿ with the following separation property: if , then there are a finite number of linear functions , such that

We show that every such set is the intersection of its radiant and co-radiant hulls. Also the union of a finite family of the sets under consideration is examined.

Keywords:

• Radiant set
• Co-radiant set
• Abstract convex set
• Min-type function
• Mathematics Subject Classifications 2000: 52A20
• 52A41

Acknowledgment

The author is very thankful to A.M. Rubinov for his interest in this work and valuable comments.