Abstract

In a three-dimensional normed space \(X\), any bounded Chebyshev set is monotone path connected if and only if one of the following two conditions holds: (1) the set of extreme points of the sphere in the dual space is dense in this sphere; (2) \(X=Y\oplus_\infty \mathbb R\) (i.e., the unit sphere of \(X\) is a cylinder).

中文翻译：

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所有有界切比雪夫集单调路径连接的三维空间

摘要

在三维赋范空间\(X\)中，任何有界切比雪夫集都是单调路径连通的，当且仅当以下两个条件之一成立： (1) 对偶空间中球体极值点的集合是稠密的在这个领域；(2) \(X=Y\oplus_\infty \mathbb R\) （即\(X\)的单位球体是圆柱体）。