Minkowski versus Euclidean rank for products of metric spaces (Q2783471)

The authors introduce a notion of the Euclidean and the Minkowski rank for arbitrary metric spaces \(M\) and study their behaviour with respect to products. While the Euclidean rank is the maximal dimension of a Euclidean space isometrically embedded in \(M\), the Minkowski rank is defined as the maximal dimension of a normed vector space that can be isometrically embedded in \(M\). It is shown that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank does not hold in general.