Best approximations of convex compact sets by balls in the Hausdorff metric

被引：1

作者：

Sosov, EN

机构：

[1] N. G. Chebotarev Mathematics and Mechanics Research Institute,

来源：

MATHEMATICAL NOTES | 2004年 / 76卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

geodesic metric space; bounded set; Hausdorff metric;

D O I：

10.1023/B:MATN.0000036759.76369.0b

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deduce an upper bound for the Hausdorff distance between a nonempty bounded set and the set of all closed balls in a strictly convex straight geodesic space X of nonnegative curvature. We prove that the set chi[M] of centers of closed balls approximating a convex compact set M subset of X in the Hausdorff metric in the best possible way is nonempty and is contained in M. Some other properties of chi[M] also are investigated.

引用

页码：209 / 218

页数：10

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