Isometric embeddings of metric \(Q\)-vector spaces into \(Q^N\)
Let \(Q\) be the field of rationals and \(W\) an \(n\)-dimensional Euclidean vector space over \(Q\). The author proves that \(W\) is isometrically embeddable in \(Q^{n+3}\) and gives an explicit algorithm for obtaining the minimum \(N\) such that \(W\) is isometrically embeddable in \(Q^N\). This answers open problems posed by \textit{H. Maehara} [Embedding a set of rational points in lower dimensions, to appear is Discrete Math. 192, 273-279 (1998; Zbl 0956.51009)].
scientific article; zbMATH DE number 1235000