Inverse semigroup of metrics on a double is fundamental

TL;DR

This paper demonstrates that the inverse group formed by equivalence classes of metrics on two copies of a space is a fundamental structure in the context of metric spaces.

Contribution

It introduces and proves the fundamental nature of the inverse group of metrics on double copies of a space.

Findings

The inverse group of metrics is fundamental.

Equivalence classes of metrics form a key algebraic structure.

The result applies to double copies of metric spaces.

Abstract

We show that the inverse group of equivalence classes of metrics on two copies of a metric space is fundamental.