Intrinsic isometries in Euclidean space

TL;DR

This paper characterizes compact metric spaces that can be intrinsically isometrically embedded into Euclidean space, showing they are exactly inverse limits of Euclidean polyhedra, thus linking geometric and topological properties.

Contribution

It establishes a precise equivalence between spaces admitting intrinsic isometries into Euclidean space and inverse limits of Euclidean polyhedra, advancing understanding of metric space embeddings.

Findings

Spaces with intrinsic isometries are inverse limits of Euclidean polyhedra

Characterization of compact metric spaces in Euclidean embeddings

Bridges geometric and topological properties of metric spaces

Abstract

I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of inverse limits of Euclidean d-polyhedra.