Differences of Convex Compact Sets in the Space of Directed Sets, Part II: Visualization of Directed Sets

R. Baier, E. Farkhi: Differences of Convex Compact Sets in the Space of Directed Sets, Part II: Visualization of Directed Sets
Set-Valued Analysis 9 (3), 247 - 272, 2001

DOI: 10.1023/A:1012009529492
MR Nummer: 1863361
Zentralblattnummer: 1097.49508
Keywords: directed sets; directed intervals; differences of convex sets and their visualization; convex analysis; interval analysis
Mathematics Subject Classification Code: 52A20 (26E25 54C60 65G30 49J53)
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Abstract:

This paper is a continuation of the author's first paper (Set-Valued Anal. 9 (2001), pp. 217-245), where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in |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.

Contents:

1. Introduction
2. Visualization of Directed Intervals
3. Visualization of Directed Sets
4. Characterization of Special Types of Directed Sets
5. Conclusions

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