The Demyanov metric and some other metrics in the family of convex sets

We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.

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Veröffentlicht in:	Central European journal of mathematics 2012, Vol.10 (6), p.2229-2239
1. Verfasser:	Rzeżuchowski, Tadeusz
Format:	Artikel
Sprache:	eng
Schlagworte:	52A20 54E50 58C06 Algebra Convex sets Convexity Demyanov metric Geometry Hausdorff metric Lie Groups Mathematics Mathematics and Statistics Metric space Number Theory Probability Theory and Stochastic Processes Research/Review Article Small changes of sets Topological Groups
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Beschreibung
Zusammenfassung:	We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
ISSN:	1895-1074 2391-5455 1644-3616 2391-5455
DOI:	10.2478/s11533-012-0129-0