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Beiträge zur Algebra und Geometrie - Contributions to Algebra and Geometry

, Volume 53, Issue 2, pp 379–397

First Online: 15 December 2011Received: 12 October 2011Accepted: 02 December 2011

Abstract

Burago et al. Graduate studies in mathematics, AMS, 2001 considered quotient metric spaces consisting of orbits with respect to some isometry groups. We extend their approach over some semigroups of transformations. We are concerned with quotient semi-metrics in spaces of generalized orbits and give conditions sufficient for these semi-metrics to be metrics. We apply our approach to hyperspaces of compact convex subsets of Euclidean n-space and to that of convex bodies, endowed, respectively, with the Hausdorff metric and with the symmetric difference metric.

KeywordsCompact convex sets Convex bodies Hausdorff metric Symmetric difference metric Quotient semi-metric Quotient metric Weakly left right divisible semigroup An erratum to this article can be found at http:-dx.doi.org-10.1007-s13366-012-0115-5.

Mathematics Subject Classification 200020M20 54E35 54E40 54E25  Download to read the full article text



Author: Agnieszka Bogdewicz - Irmina Herburt - Maria Moszyńska

Source: https://link.springer.com/







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