# Density of generic metric spaces in the Gromov--Hausdorff class

## TL;DR

This paper proves that in the space of all metric spaces equipped with the Gromov-Hausdorff distance, generic metric spaces are dense, meaning they can be approximated arbitrarily closely by other metric spaces.

## Contribution

It establishes the density of generic metric spaces within the Gromov-Hausdorff class, a fundamental property in metric geometry.

## Key findings

- Generic metric spaces are dense in the Gromov-Hausdorff space.
- The result applies to the proper class of all metric spaces.
- Provides foundational insight into the structure of metric space classes.

## Abstract

In this paper we prove that generic metric spaces are everywhere dense in the proper class of all metric spaces endowed with the Gromov-Hausdorff distance.