A continuity criterion for Steiner-type ratios in the Gromov-Hausdorff space |
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| Authors: | A S Pakhomova |
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| Institution: | 1. Moscow State University, Moscow, Russia
2. Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Yaroslavl, Russia
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| Abstract: | A criterion for the continuity of the Steiner ratio, the Steiner subratio, and the Steiner-Gromov ratio in the space of all compact metric spaces with the Gromov-Hausdorff metric is obtained. It is also proved that these functions are upper semicontinuous. |
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