Equilateral sets in the l1 sum of Euclidean spaces

被引：0

作者：

Lin, Aaron ^{[1
]}

机构：

[1] London Sch Econ & Polit Sci, Dept Math, London, England

来源：

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2020年 / 61卷 / 01期

关键词：

Equilateral sets; Normed spaces; Regular simplices;

D O I：

10.1007/s13366-019-00455-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let En denote the (real) n-dimensional Euclidean space. It is not known whether an equilateral set in the 1 sum of Ea and Eb, denoted here as Ea. 1 Eb, has maximum size at least dim( Ea. 1 Eb) + 1 = a + b + 1 for all pairs of a and b. We show, via some explicit constructions of equilateral sets, that this holds for all a 27, as well as some other instances.

引用

页码：151 / 155

页数：5

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