On the hull operator

Abstract

Hull operators, such as the closure, the linear, the convex, the positive hull operator, can be studied starting from a few fundamental properties. This paper deals with an operator j h deduced from a hull operator h, which e.g. characterizes the isolated points in case h is the topological closure operator and the extreme points in case h is the convex hull operator. By a slight generalization a comparable relation can be established between the isolated components and the extreme rays, if the hull operator is respectively the topological closure operator or the positive hull operator. § 1 is introductory. In § 2 j h is studied and § 3 deals with the above-mentioned generalization. ℘(U) will be used in the subsequent paragraphs to denote the set of subsets of the set U.