Isometric embeddings of pretangent spaces in E^n

TL;DR

This paper explores conditions under which infinitesimal metric spaces, specifically pretangent spaces, can be isometrically embedded into finite-dimensional Euclidean spaces, extending classical embedding results.

Contribution

It provides infinitesimal analogs of classical theorems, establishing new existence conditions for isometric embeddings of pretangent spaces into Euclidean spaces.

Findings

Established conditions for isometric embeddings of pretangent spaces.

Extended classical embedding theorems to infinitesimal settings.

Contributed to the understanding of metric space embeddings at small scales.

Abstract

We prove some infinitesimal analogs of classical results of Menger, Schoenberg and Blumenthal giving the existence conditions for isometric embeddings of metric spaces in the finite-dimensional Euclidean spaces.