A continuity criterion for Steiner-type ratios in the Gromov-Hausdorff space

被引：4
|
作者：
Pakhomova, A. S. [1 ,2 ]
机构：
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
[2] Yaroslavl State Univ, Delone Lab Discrete & Computat Geometry, Yaroslavl, Russia
来源：
MATHEMATICAL NOTES | 2014年 / 96卷 / 1-2期
基金：
俄罗斯基础研究基金会;
关键词：
Steiner ratio; Steiner subratio; Steiner-Gromov ratio; Gromov-Hausdorff metric; Gromov-Hausdorff space; minimal filling; Steiner minimal tree;
D O I：
10.1134/S0001434614070128
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：130 / 139
页数：10
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