Differences of convex compact sets in the space of directed sets. II: Visualization of directed sets. (English) Zbl 1097.49508

Baier, Robert; Farkhi, Elza M.

Set-Valued Anal. 9, No. 3, 247-272 (2001).

Summary: This paper is a continuation of the authors’ first paper [Set-Valued Anal. 9, No. 3, 217-245 (2001; Zbl 1097.49507)], where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in \(\mathbb R^n\) is embedded. A visualization of directed sets and of differences of convex compact sets is presented and its geometrical components and properties are studied. The three components of the visualization are compared with other known differences of convex compact sets.

MSC:

49J53	Set-valued and variational analysis
52A20	Convex sets in \(n\) dimensions (including convex hypersurfaces)
54C60	Set-valued maps in general topology
65G30	Interval and finite arithmetic

Keywords:

directed sets; directed intervals; differences of convex sets and their visualization; convex analysis; interval analysis

Citations:

Zbl 1097.49507