Isometric embedding of finite ultrametric spaces in Banach spaces
Recall that a metric space \((X, d)\) is called ultrametric (or isosceles, or non-Archimedian) if \(d(x, z)\leq\max\{d(x, y),d(y, z)\}\) for all \(x,y,z\in X\). It was shown by \textit{B. Fichet} in [Classification and related methods of data analysis, Proc. 1st Conf. IFCS, Aachen/FRG 1987, 439--444 (1984; Zbl 0734.62002)] that every finite ultrametric space can be isometrically embedded into the Banach space \(l_p\) for each \(p\in[1,\infty]\). In this interesting paper it is shown that, in fact, every finite ultrametric space can be isometrically embedded into every infinite-dimensional Banach space.
scientific article; zbMATH DE number 2117940
scientific article