Pairs of Compact Convex Sets : Fractional Arithmetic with Convex Sets /
The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Rådström-Hörmander Theory. Minimal pairs of compact...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands,
2002.
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| Series: | Mathematics and its applications ;
548. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Rådström-Hörmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the Rådström-Hörmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xii, 295 pages) |
| ISBN: | 9789401599207 (electronic bk.) 9401599203 (electronic bk.) |