Expansive maps are isometries

TL;DR

This paper proves that any expansive map defined on a dense subset of a compact metric space must be an isometry, highlighting a strong rigidity property of such maps.

Contribution

It establishes that expansive maps on dense subsets of compact metric spaces are necessarily isometries, a novel rigidity result.

Findings

Expansive maps on dense subsets are isometries.

The result applies to compact metric spaces.

Expansiveness implies isometry under the given conditions.

Abstract

We show that expansive maps from a dense subset of a compact metric space into the metric space itself are isometries