On Nearly Equilateral Simplices and Nearly l∞ Spaces

Canadian mathematical bulletin

Gennadiy Averkov¹ 

[1] Institute for Mathematical Optimization, Faculty of Mathematics, University of Magdeburg, Magdeburg, Germany

关键词: graph;    $(g;    f)$-factor;    $(g;    f;    n)$-critical graph;    binding number;   

DOI  :  10.4153/CMB-2010-055-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

By $extrm{d}(X,Y)$ we denote the (multiplicative) Banach--Mazur distance between two normed spaces $X$ and $Y.$ Let $X$ be an $n$-dimensional normed space with $extrm{d}(X,ell_infty^n) le 2,$ where $ell_infty^n$ stands for $mathbb{R}^n$ endowed with the norm $|(x_1,dots,x_n)|_infty := max {|x_1|,dots, |x_n| }.$ Then every metric space $(S,ho)$ of cardinality $n+1$ with norm $ho$ satisfying the condition $max D / min D le 2/ extrm{d}(X,ell_infty^n)$ for $D:={ ho(a,b) : a, b in S,a e b}$ can be isometrically embedded into $X.$

【 授权许可】

Unknown