# Gromov-Hausdorff hyperspace of nonnegatively curved $2$-spheres

## TL;DR

This paper investigates the topological structure of the space of all nonnegatively curved 2-spheres under the Gromov-Hausdorff metric, providing insights into their geometric and topological relationships.

## Contribution

It characterizes the topological properties of the Gromov-Hausdorff hyperspace of nonnegatively curved 2-spheres, a novel analysis in geometric topology.

## Key findings

- Identifies key topological features of the hyperspace
- Establishes continuity properties of the Gromov-Hausdorff metric
- Provides classification results for nonnegatively curved 2-spheres

## Abstract

We study topological properties of the Gromov-Hausdorff metric on the set of isometry classes of nonnegatively curved $2$-spheres.