Isometric embeddings of pretangent spaces in \( E^n\) (Q351259)

The aim of this paper is to give different criteria for the isometric embeddability of pretangent metric spaces in the real \(n\)-dimensional Euclidean space \(E^{n}\). Note that the definition of pretangent and tangent metric spaces to an arbitrary metric space was introduced by \textit{O. Dovgoshey} and \textit{O. Martio} in [``Tangent spaces to metric spaces'', Reports in Math., Helsinki Univ. 480 (2008)], for studies of generalized differentiation on metric spaces.NEWLINENEWLINEIn particular the authors extend the classical results of isometric embeddability of metric spaces in \(E^{n}\) of K. Menger, I. Schoenberg and L. Blumenthal to pretangent metric spaces. To this purpose they introduce a \textit{Transfer Principle} which provides, in some cases, \textsl{the ``automatic translation'' of global properties of pretangent spaces into the limit relations defined in the initial metric spaces}. However, in the case of Blumenthal's embedding theorem the Transfer Principle does not seem to be applicable.